1 Introduction ANSWERS TO MULTIPLE CHOICE QUESTIONS 1. Using a calculator to acception the prolixity by the width confers a inexperienced apology of 6783 m 2 , yet this apology must be rounded to comprise the identical calculate of indicationi? confused-talk ? gures as the inferiointerim respectful constituent in the emanation. The inferiointerim respectful constituent is the prolixity, which comprises either 2 or 3 indicationi? confused-talk ? gures, holding on whether the luxuriance naught is indicationi? confused-talk or is morals manifestationd barely to dispose the decimal apex. Pretentious the prolixity comprises 3 indicationi? confused-talk ? gures, apology (c) soundly expresses the area as 6. 78 ? 10 3 m 2 .
However, if the prolixity comprises barely 2 indicationi? confused-talk ? gures, apology (d) confers the improve development as 6. 8 ? 10 3 m 2 . Twain apologys (d) and (e) could be physically meaningful. Apologys (a), (b), and (c) must be meaningshort past quantities can be presumed or withdrawed barely if they keep the identical bulk. According to Newton’s remedy principle, Cece = concretion ? succor . Thus, the items of Cece must be the emanation of the items of concretion (kg) and the items of succor ( m s 2 ). This concedes kg ? m s 2, which is apology (a). The calculator confers an apology of 57. 573 ce the combine of the 4 dedicated calculates.
However, this combine must be rounded to 58 as dedicated in apology (d) so the calculate of decimal establishs in the development is the identical (zero) as the calculate of decimal establishs in the integer 15 (the promise in the combine compriseing the inferiointerim calculate of decimal establishs). The exactd intercharge is dedicated by: ? 1 000 mm ? ? 1. 00 cubitus ? h = ( 2. 00 m ) ? ?? ? = 4. 49 cubiti ? 1. 00 m ? ? 445 mm ? This development corresponds to apology (c). 6. The dedicated area (1 420 ft 2 ) comprises 3 indicationi? confused-talk ? gures, pretentious that the luxuriance naught is manifestationd barely to dispose the decimal apex. The intercharge of this appraise to balance meters is dedicated by: 1. 00 m ? 2 2 2 A = (1. 2 ? 10 3 ft 2 ) ? ? ? = 1. 32 ? 10 m = 132 m ? 3. 281 ft ? Referablee that the development comprises 3 indicationi? confused-talk ? gures, the identical as the calculate of indicationi? confused-talk ? gures in the inferiointerim respectful constituent manifestationd in the regard. This development paires apology (b). 7. You canrefertelling subjoin, withdraw, or equate a calculate apples and a calculate of days. Thus, the apology is yes ce (a), (c), and (e). However, you can acception or entireot a calculate of apples and a calculate of days. Ce specimen, you dominion entireot the calculate of apples by a calculate of days to ? nd the calculate of apples you could munch per day. In combinemary, the apologys are (a) yes, (b) no, (c) yes, (d) no, and (e) es. 2 2. 3. 4. 5. 1 http://helpyoustudy. info 2 Chapter 1 8. The dedicated Cartesian coordinates are x = ? 5. 00, and y = 12. 00 , with the inferiointerim respectful compriseing 3 indicationi? confused-talk ? gures. Referablee that the speci? ed apex (with x < 0 and y > 0 ) is in the remedy quadrant. The intercharge to polar coordinates is then dedicated by: r = x 2 + y 2 = ( ? 5. 00 ) + (12. 00 ) = 13. 0 2 2 tan ? = y 12. 00 = = ? 2. 40 x ? 5. 00 and ? = tan ? 1 ( ? 2. 40 ) = ? 67. 3° + 180° = 113° Referablee that 180° was presumed in the ultimate tramp to concede a remedy quadrant leaning. The improve apology is coercion-this-reason (b) (13. 0, 113°). 9. Doing configurational decomcollocation on the ? st 4 dedicated exquisites concedes: (a) [ v] ?t ? ? ? 2 = LT L = 3 T2 T (b) [ v] ?x2 ? ? ? = LT = L? 1T ? 1 L2 (c) ? v 2 ? ( L T )2 L2 T 2 L2 ? ?= = = 3 T T T [t ] (d) ? v 2 ? ( L T )2 L2 T 2 L ? ?= = = 2 L L T [ x] Past succor has items of prolixity entireotd by period balanced, it is beholdn that the proportion dedicated in apology (d) is harmonious with an countenance concedeing a appraise ce succor. 10. The calculate of gallons of gasooutthread she can alienation is # gallons = entirety price 33 Euros ? exact per gallon ? Euros ? ? 1 L ? ? ? 1. 5 ?? L ? ? 1 quart ? ? ? ? ? 5 gal ? 4 quarts ? ? 1 gal ? ? ? ? ? so the improve apology is (b). 1. The top illustrative is pretencen in the plan at the suitable. h From this, mark that tan 26° = , or 45 m h = ( 45 m ) tan 26° = 22 m 26 h Thus, the improve apology is (a). 12. 45 m Referablee that we may transcribe 1. 365 248 0 ? 10 7 as 136. 524 80 ? 10 5. Thus, the inexperienced apology, including the hesitation, is x = (136. 524 80 ± 2) ? 10 5. Past the ? nal apology should comprise enbore the digits we are secure of and sundericular thinkd digit, this development should be rounded and displayed as 137 ? 10 5 = 1. 37 ? 10 7 (we are secure of the 1 and the 3, yet keep hesitation encircling the 7). We behold that this apology has three indicationi? confused-talk ? ures and exquisite (d) is improve. ANSWERS TO EVEN NUMBERED CONCEPTUAL QUESTIONS 2. Moleculeic clocks are infamousd on the electromagnetic waves that molecules extrude. Too, pulsars are extremely established astronomical clocks. http://helpyoustudy. info Introduction 3 4. (a) (b) (c) ~ 0. 5 lb ? 0. 25 kg or ~10 ? 1 kg ~ 4 lb ? 2 kg or ~10 0 kg ~ 4000 lb ? 2000 kg or ~10 3 kg 6. Let us presume the molecules are bungerative globes of bisection 10? 10 m. Then, the capacity of each molecule is of the regulate of 10? 30 m3. (Aggravate undoubtfully, capacity = 4? r 3 3 = ? d 3 6 . ) Coercion-this-reason, past 1 cm 3 = 10 ? 6 m 3, the calculate of molecules in the 1 cm3 bungerative is on the regulate of 10 ? 10 ? 30 = 10 24 molecules. A aggravate keep-aaim regard would exact enlightenment of the blindness of the bungerative and the concretion of each molecule. However, our think agrees with the aggravate keep-aaim regard to amid a constituent of 10. Realistically, the barely prolixitys you dominion be operative to confirm are the prolixity of a footbenbore ? eld and the prolixity of a issue? y. The barely period interims matter to veri? cation would be the prolixity of a day and the period natant usual heartbeats. In the metric rule, items disagree by powers of ten, so it’s very managetelling and respectful to turn from sundericular item to another. 8. 10. ANSWERS TO EVEN NUMBERED PROBLEMS . 4. 6. 8. 10. 12. 14. 16. 18. (a) L T2 (b) L Enbore three equations are configurationally inexact. (a) (a) (a) (a) (a) kg ? m s 22. 6 3. 00 ? 108 m s 346 m 2 ± 13 m 2 797 (b) (b) (b) (b) (b) Ft = p 22. 7 2 . 997 9 ? 108 m s 66. 0 m ± 1. 3 m 1. 1 (c) 17. 66 (c) (c) 22. 6 is aggravate relioperative 2. 997 925 ? 108 m s 3. 09 cm s (a) (b) (c) (d) 5. 60 ? 10 2 km = 5. 60 ? 10 5 m = 5. 60 ? 10 7 cm 0. 491 2 km = 491. 2 m = 4. 912 ? 10 4 cm 6. 192 km = 6. 192 ? 10 3 m = 6. 192 ? 10 5 cm 2. 499 km = 2. 499 ? 10 3 m = 2. 499 ? 10 5 cm 20. 22. 24. 26. 10. 6 km L 9. 2 nm s 2 . 9 ? 10 2 m 3 = 2 . 9 ? 108 cm 3 2 . 57 ? 10 6 m 3 ttp://helpyoustudy. info 4 Chapter 1 28. 30. 32. 34. ? 108 tramps ~108 nation with indifferents on any dedicated day (a) (a) 4. 2 ? 10 ? 18 m 3 ? 10 29 prokaryotes (b) (b) ~10 ? 1 m 3 ~1014 kg (c) ~1016 cells (c) The very wide concretion of prokaryotes implies they are essential to the biosphere. They are binding ce ? xing carbon, submissive oxygen, and disturbance up pollutants, natant divers other biological roles. Proportionnals hold on them! 36. 38. 40. 42. 44. 46. 48. 2. 2 m 8. 1 cm ? s = r12 + r22 ? 2r1r2 cos (? 1 ? ?2 ) 2. 33 m (a) 1. 50 m (b) 2. 60 m 8. 60 m (a) and (b) (c) 50. 52. 54. y= (a) y x = tan 12. 0°, y ( x ? . 00 km ) = tan 14. 0° d ? tan ? ? tan ? tan ? ? tan ? 1. 609 km h (b) 88 km h (d) 1. 44 ? 10 3 m (c) 16 km h Presumes population of 300 darling, mediocre of 1 can week per idiosyncratic, and 0. 5 oz per can. (a) ? 1010 cans yr 7. 14 ? 10 ? 2 gal s A2 A1 = 4 ? 10 2 yr (b) (b) (b) (b) ? 10 5 tons yr 2. 70 ? 10 ? 4 m 3 s V2 V1 = 8 ? 10 4 periods (c) 1. 03 h 56. 58. 60. 62. (a) (a) (a) ? 10 4 globes yr. Presumes 1 past benbore per hitter, 10 hitters per inning, 9 innings per diversion, and 81 diversions per year. http://helpyoustudy. info Introduction 5 PROBLEM SOLUTIONS 1. 1 Substituting bulk into the dedicated equation T = 2? ionshort perpetual, we keep g , and recognizing that 2? is a dimen- [T ] = [ ] [ g] or T= L = L T2 T2 = T Thus, the bulk are harmonious . 1. 2 (a) From x = Bt2, we ? nd that B = [ B] = [ x] L = 2 [t 2 ] T x . Thus, B has items of t2 (b) If x = A ungodliness ( 2? ft ), then [ A] = [ x ] [ungodliness ( 2? ft )] Yet the ungodlinesse of an leaning is a configurationshort proportion. Coercion-this-reason, [ A] = [ x ] = L 1. 3 (a) The items of capacity, area, and crisis are: [V ] = L3, [ A] = L2 , and [h] = L We then mark that L3 = L2 L or [V ] = [ A][h] Thus, the equation V = Ah is configurationally improve . (b) Vcylinder = ? R 2 h = (? R 2 ) h = Ah , where A = ?

R 2 Vrectangular buffet = wh = ( w ) h = Ah, where A = w = prolixity ? width 1. 4 (a) L ML2 2 2 m v 2 = 1 m v0 + mgh, [ m v 2 ] = [ m v0 ] = M ? ? = 2 ? ? 2 T ? T? 1 2 L ? M L suitableness ? mgh ? = M ? 2 ? L = . Thus, the equation is configurationally inimprove . ? ? ? T ? T ? In the equation 1 2 2 (b) L L yet [at 2 ] = [a][t 2 ] = ? 2 ? ( T 2 ) = L. Future, this equation ? ? T ? T ? is configurationally inimprove . In v = v0 + at 2, [ v] = [ v0 ] = L In the equation ma = v 2, we behold that [ ma] = [ m][a] = M ? 2 ? ?T Coercion-this-reason, this equation is too configurationally inimprove . 2 ? = ML , suitableness [ v 2 ] = ? L ? = L . ? ? ? 2 T2 ? T ? T? 2 (c) . 5 From the boundshort destroyer principle, the perpetual G is G = Fr 2 Mm. Its items are then [G ] = [ F ] ? r 2 ? ( kg ? m s2 ) ( m 2 ) m3 ? ?= = kg ? kg kg ? s 2 [ M ][ m ] http://helpyoustudy. info 6 Chapter 1 1. 6 (a) Solving KE = p2 ce the availum, p, confers p = 2 m ( KE ) where the numeral 2 is a 2m configurationshort perpetual. Configurational decomcollocation confers the items of availum as: [ p] = [ m ][ KE ] = M ( M ? L2 T 2 ) = M 2 ? L2 T 2 = M ( L T ) Coercion-this-reason, in the SI rule, the items of availum are kg ? ( m s ) . (b) Referablee that the items of cece are kg ? m s 2 or [ F ] = M ? L T 2 . Then, mark that [ F ][ t ] = ( M ?
L T 2 ) ? T = M ( L T ) = [ p ] From this, it follows that cece multitudinous by period is proportional to availum: Ft = p . (Behold the cessationraintce–momentum theorem in Chapter 6, F ? ?t = ? p , which says that a perpetual cece F multitudinous by a continuance of period ? t resemblings the qualify in availum, ? p. ) 1. 7 1. 8 Area = ( prolixity ) ? ( width ) = ( 9. 72 m )( 5. 3 m ) = 52 m 2 (a) Computing ( 8) 3 extraneously rounding the intervening development concedes ( 8) (b) 3 = 22. 6 to three indicationi? confused-talk ? gures. Rounding the intervening development to three indicationi? confused-talk ? gures concedes 8 = 2. 8284 > 2. 83 Then, we succeed ( 8) 3 = ( 2. 83) = 22. 7 to three indicationi? ant ? gures. 3 (c) 1. 9 (a) (b) (c) (d) The apology 22. 6 is aggravate relioperative consequently rounding in keep-akeep-adistribute (b) was carried extinguished too precedently-long. 78. 9 ± 0. 2 has 3 indicationificonfused-talk figures with the hesitation in the tenths collocation. 3. 788 ? 10 9 has 4 indicationificonfused-talk figures 2. 46 ? 10 ? 6 has 3 indicationificonfused-talk figures 0. 003 2 = 3. 2 ? 10 ? 3 has 2 indicationificonfused-talk figures . The bcareer naughts were cemerly middle barely to collocation the decimal. 1. 10 c = 2 . 997 924 58 ? 108 m s (a) (b) (c) Rounded to 3 indicationi? confused-talk ? gures: c = 3. 00 ? 108 m s Rounded to 5 indicationi? confused-talk ? gures: c = 2 . 997 9 ? 108 m s Rounded to 7 indicationi? confused-talk ? gures: c = 2 . 997 925 ? 08 m s 1. 11 Mark that the prolixity = 5. 62 cm, the width w = 6. 35 cm, and the crisis h = 2. 78 cm enbore comprise 3 indicationi? confused-talk ? gures. Thus, any emanation of these quantities should comprise 3 indicationi? confused-talk ? gures. (a) (b) w = ( 5. 62 cm )( 6. 35 cm ) = 35. 7 cm 2 V = ( w ) h = ( 35. 7 cm 2 ) ( 2. 78 cm ) = 99. 2 cm 3 abided on present page http://helpyoustudy. info Introduction 7 (c) wh = ( 6. 35 cm )( 2. 78 cm ) = 17. 7 cm 2 V = ( wh ) = (17. 7 cm 2 ) ( 5. 62 cm ) = 99. 5 cm 3 (d) In the rounding manner, smenbore aggregates are either presumed to or withdrawed from an apology to indemnify the rules of indicationi? confused-talk ? gures.
Ce a dedicated rounding, disagreeent smenbore adjustments are made, introducing a undoubtful aggregate of randomness in the ultimate indicationi? confused-talk digit of the ? nal apology. 2 2 2 A = ? r 2 = ? (10. 5 m ± 0. 2 m ) = ? ?(10. 5 m ) ± 2 (10. 5 m )( 0. 2 m ) + ( 0. 2 m ) ? ? ? 1. 12 (a) Recognize that the ultimate promise in the brackets is insigni? confused-talk in similitude to the other brace. Thus, we keep A = ? ?110 m 2 ± 4. 2 m 2 ? = 346 m 2 ± 13 m 2 ? ? (b) 1. 13 C = 2? r = 2? (10. 5 m ± 0. 2 m ) = 66. 0 m ± 1. 3 m The inferiointerim respectful configuration of the buffet has bcareer indicationi? confused-talk ? gures. Thus, the capacity (emanation of the three bulk) produce comprise barely bcareer indicationi? confused-talk ? ures. V = ? w ? h = ( 29 cm )(17. 8 cm )(11. 4 cm ) = 5. 9 ? 10 3 cm 3 1. 14 (a) The combine is rounded to 797 consequently 756 in the promises to be presumed has no collocations aggravate the decimal. 0. 003 2 ? 356. 3 = ( 3. 2 ? 10 ? 3 ) ? 356. 3 = 1. 14016 must be rounded to 1. 1 consequently 3. 2 ? 10 ? 3 has barely bcareer indicationi? confused-talk ? gures. 5. 620 ? ? must be rounded to 17. 66 consequently 5. 620 has barely lewd indicationi? confused-talk ? gures. (b) (c) 1. 15 5 280 ft ? ? 1 gauge ? 8 d = ( 250 000 mi ) ? ? ?? ? = 2 ? 10 gauges ? 1. 000 mi ? ? 6 ft ? The apology is sgibberish to sundericular indicationi? confused-talk ? gure consequently of the faultlessness to which the intercharge from gauges to feet is dedicated. . 16 v= t = 186 furlongs 1 cetnight ? 1 cetnight ? ? 14 days ? ? ? 1 day ? ? 220 yds ?? ?? ? ? 8. 64 ? 10 4 s ? ? 1 furhanker ?? ?? ? ? 3 ft ?? ? ? 1 yd ?? ? ? 100 cm ? ?? ? ? 3. 281 ft ? ? ? giving v = 3. 09 cm s ? ? 3. 786 L ?? ? ? 1 gal ?? ? ? 10 3 cm 3 ? ? 1 m 3 ? = 0. 204 m 3 ?? ? ? 1 L ? ? 10 6 cm 3 ? ?? ? ? 1. 17 ? 9 gal 6. 00 firkins = 6. 00 firkins ? ? 1 firkin ? (a) 1. 18 1. 609 km ? 2 5 7 = ( 348 mi ) ? 6 ? ? = 5. 60 ? 10 km = 5. 60 ? 10 m = 5. 60 ? 10 cm ? 1. 000 mi ? ? 1. 609 km ? 4 h = (1 612 ft ) ? 2 ? = 0. 491 2 km = 491. 2 m = 4. 912 ? 10 cm 5 280 ft ? ? ? 1. 609 km ? 3 5 h = ( 20 320 ft ) ? = 6. 192 km = 6. 192 ? 10 m = 6. 192 ? 10 cm 5 280 ft ? ? (b) (c) abided on present page http://helpyoustudy. info 8 Chapter 1 (d) ? 1. 609 km ? 3 5 d = (8 200 ft ) ? ? = 2 . 499 km = 2 . 499 ? 10 m = 2 . 499 ? 10 cm ? 5 280 ft ? In (a), the apology is sgibberish to three indicationi? confused-talk ? gures consequently of the faultlessness of the cemer reasons appraise, 348 miles. In (b), (c), and (d), the apologys are sgibberish to lewd indicationi? confused-talk ? gures consequently of the faultlessness to which the kilometers-to-feet intercharge constituent is dedicated. 1. 19 v = 38. 0 m ? 1 km ? ? 1 mi ? ? 3 600 s ? ?? ? = 85. 0 mi h ?? ? s ? 10 3 m ? ? 1. 609 km ? 1 h ? Yes, the driver is big the acceleadmonish designation by 10. 0 mi h . mi ? 1 km ? ? 1 gal ? ? = 10. 6 km L ?? ? gal ? 0. 621 mi ? ? 3. 786 L ? ? ? 1. 20 power = 25. 0 r= 1. 21 (a) (b) (c) bisection 5. 36 in ? 2. 54 cm ? = ? ? = 6. 81 cm 2 2 ? 1 in ? 2 A = 4? r 2 = 4? ( 6. 81 cm ) = 5. 83 ? 10 2 cm 2 V= 4 3 4 3 ? r = ? ( 6. 81 cm ) = 1. 32 ? 10 3 cm 3 3 3 ? ? 1 h ? ? 2. 54 cm ? ? 10 9 nm ? ?? ? 3 600 s ? ? 1. 00 in ? ? 10 2 cm ? = 9. 2 nm s ? ?? ?? ?? 1. 22 ? 1 in ? ? 1 day admonish = ? ? 32 day ? ? 24 h ?? ? ?? This resources that the proteins are assembled at a admonish of divers flakes of molecules each remedy! 1. 3 ? m ? ? 3 600 s ? ? 1 km ? ? 1 mi ? 8 c = ? 3. 00 ? 10 8 ?? ?? ?? ? = 6. 71 ? 10 mi h s ? ? 1 h ? ? 10 3 m ? ? 1. 609 km ? ? ? 2 . 832 ? 10 ? 2 m3 ? Capacity of issue = ( 50. 0 ft )( 26 ft )(8. 0 ft ) ? ? 1 ft 3 ? ? ? 100 cm ? = 2 . 9 ? 10 2 m3 = ( 2 . 9 ? 10 2 m3 ) ? = 2 . 9 ? 10 8 cm3 ? 1m ? ? 1. 25 1. 26 2 2 ? 1 m ? ?? 43 560 ft ? ? 1 m ? ? ?? ? = 3. 08 ? 10 4 m3 Capacity = 25. 0 acre ft ? ? ? ? ? 3. 281 ft ? ?? 1 acre ? ? 3. 281 ft ? ? ? ? ? 1 Capacity of pyramid = ( area of infamous )( crisis ) 3 3 1. 24 ( ) = 1 ? (13. 0 acres )( 43 560 ft 2 acre ) ? ( 481 ft ) = 9. 08 ? 10 7 f ? 3? ? 2 . 832 ? 10 ? 2 m3 ? 3 = ( 9. 08 ? 10 7 ft 3 ) ? 5 ? = 2 . 57 ? 10 m 1 ft3 ? ? 1. 27 Capacity of cube = L 3 = 1 quart (Where L = prolixity of sundericular distributey of the cube. ) ? 1 gallon ? ? 3. 786 liter ? ? 1000 cm3 ? i = 947 cm3 Thus, L 3 = 1 quart ? ?? ? 4 quarts ? ? 1 gallon ? ? 1 liter ? ? ?? ? ? ( ) and L = 3 947 cm3 = 9. 82 cm http://helpyoustudy. info Introduction 9 1. 28 We think that the prolixity of a tramp ce an mediocre idiosyncratic is encircling 18 inches, or knottyly 0. 5 m. Then, an think ce the calculate of tramps exactd to pilgreffigy a interintervenience resembling to the enclosure of the Earth would be N= or 3 2? ( 6. 38 ? 10 6 m ) Enclosure 2?
RE = ? ? 8 ? 10 7 tramps 0. 5 m tramp Tramp Prolixity Tramp Prolixity N ? 108 tramps 1. 29. We presume an mediocre respiration admonish of encircling 10 breaths/minute and a normal morals p of 70 years. Then, an think of the calculate of breaths an mediocre idiosyncratic would procure in a moralsperiod is ? ? breaths ? 10 7 ? min n = ? 10 ( 70 yr ) ? 3. 156 ? yr s ? ? 160 s ? = 4 ? 108 breaths ? ? ?? ? min ? 1 ? ? ?? ? or n ? 108 breaths 1. 30 We presume that the mediocre idiosyncratic seizees a incontrariant twice a year and is valetudinarian an mediocre of 7 days (or 1 week) each period. Thus, on mediocre, each idiosyncratic is valetudinarian ce 2 weeks extinguished of each year (52 weeks).
The enjoylihood that a keep-aaim idiosyncratic produce be valetudinarian at any dedicated period resemblings the percentage of period that idiosyncratic is valetudinarian, or enjoylihood of valetudinarianness = 2 weeks 1 = 52 weeks 26 The population of the Earth is resemblely 7 jawion. The calculate of nation expected to keep a incontrariant on any dedicated day is then 1 Calculate valetudinarian = ( population )( enjoylihood of valetudinarianness ) = ( 7 ? 10 9 ) ? ? = 3 ? 108 or ? 108 ( ? ? ? 26 ? 1. 31 (a) Presume that a normal intestinal believe has a prolixity of encircling 7 m and mediocre bisection of 4 cm. The thinkd entirety intestinal capacity is then ? ?d 2 ? ? ( 0. 04 m ) Ventirety = A = ? ( 7 m ) = 0. 009 m 3 ? 4 ? 4 ? 2 The resemble capacity shackled by a ungodlinessgle bacterium is Vbacteria ? ( normal prolixity lamina ) = (10 ? 6 m ) = 10 ? 18 m 3 3 3 If it is presumed that bacteria busy sundericular hundredth of the entirety intestinal capacity, the think of the calculate of microorganisms in the proportionnal intestinal believe is n= (b) 3 Ventirety 100 ( 0. 009 m ) 100 = = 9 ? 1013 or n ? 1014 10 ? 18 m 3 Vbacteria The wide appraise of the calculate of bacteria thinkd to purposeure in the intestinal believe resources that they are probably refertelling hazardous. Intestinal bacteria aid classify maintenance and procure essential nutrients. Proportionnals and bacteria relish a mutually bene? ial symbiotic proportionship. Vcell = 3 4 3 4 ? r = ? (1. 0 ? 10 ? 6 m ) = 4. 2 ? 10 ? 18 m 3 3 3 1. 32 (a) (b) Consider your collectiveness to be a cylinder having a radius of encircling 6 inches (or 0. 15 m) and a crisis of encircling 1. 5 meters. Then, its capacity is Vcollectiveness = Ah = (? r 2 ) h = ? ( 0. 15 m ) (1. 5 m ) = 0. 11 m 3 or ? 10 ? 1 m 3 2 abided on present page http://helpyoustudy. info 10 Chapter 1 (c) The think of the calculate of cells in the collectiveness is then n= Vcollectiveness Vcell = 0. 11 m 3 = 2. 6 ? 1016 or ? 1016 ? 18 3 4. 2 ? 10 m 1. 33 A reasonoperative suspect ce the bisection of a bore dominion be 3 ft, with a enclosure (C = 2? r = ?
D = interintervenience pilgrimages per vicissitude) of encircling 9 ft. Thus, the entirety calculate of vicissitudes the bore dominion create is n= entirety interintervenience pilgrimageed ( 50 000 mi )( 5 280 ft mi ) = 3 ? 10 7 rev, or ~ 10 7 rev = interintervenience per vicissitude 9 ft rev 1. 34 Apologys to this exaltation produce disagree, holdent on the presumptions sundericular creates. This disconnection presumes that bacteria and other prokaryotes busy resemblely sundericular ten-millionth (10? 7) of the Earth’s capacity, and that the blindness of a prokaryote, enjoy the blindness of the proportionnal collectiveness, is resemblely resembling to that of steep (103 kg/m3). (a) thinkd calculate = n = Ventirety Vsepareprimand prokaryote 10 )V ? ?7 Earth Vsepareprimand prokaryote (10 )(10 m ) ? ? (prolixity lamina) (10 m ) ?7 3 Earth ? 7 6 3 ? 6 3 (10 ) R 3 ? 10 29 (b) (c) 3 kg ? ? ? ? mentirety = ( blindness )( entirety capacity) ? ?steep ? nVsepareprimand ? = ? 10 3 3 ? (10 29 )(10 ? 6 m ) ? 1014 kg ? ? prokaryote ? ? m The very wide concretion of prokaryotes implies they are essential to the biosphere. They are binding ce ? xing carbon, submissive oxygen, and disturbance up pollutants, natant divers other biological roles. Proportionnals hold on them! x = r cos? = 2 . 5 m cos 35° = 2. 0 m 1. 35 The x coordinate is root as and the y coordinate ) y = r ungodliness? = ( 2 . 5 m ) ungodliness 35° = 1. m ( 2 1. 36 The x interintervenience extinguished to the ? y is 2. 0 m and the y interintervenience up to the ? y is 1. 0 m. Thus, we can manifestation the Pythagorean theorem to ? nd the interintervenience from the source to the ? y as d = x 2 + y2 = ( 2. 0 m ) + (1. 0 m ) 2 = 2. 2 m 1. 37 The interintervenience from the source to the ? y is r in polar coordinates, and this was root to be 2. 2 m in Exaltation 36. The leaning ? is the leaning natant r and the conformtelling regard outoutthread (the x axis in this instance). Thus, the leaning can be root as tan ? = y 1. 0 m = = 0. 50 x 2. 0 m and ? = tan ? 1 ( 0. 50 ) = 27° The polar coordinates are r = 2. 2 m and ? = 27 ° 1. 8 The x interintervenience natant the bcareer apexs is ? x = x2 ? x1 = ? 3. 0 cm ? 5. 0 cm = 8. 0 cm and the y interintervenience natant them is ? y = y2 ? y1 = 3. 0 cm ? 4. 0 cm = 1. 0 cm. The interintervenience natant them is root from the Pythagorean theorem: d= 1. 39 ? x + ? y = (8. 0 cm ) + (1. 0 cm ) = 2 2 2 2 65 cm 2 = 8. 1 cm Refer to the Figure dedicated in Exaltation 1. 40 under. The Cartesian coordinates ce the bcareer dedicated apexs are: x1 = r1 cos ? 1 = ( 2. 00 m ) cos 50. 0° = 1. 29 m y1 = r1 ungodliness ? 1 = ( 2. 00 m ) ungodliness 50. 0° = 1. 53 m x2 = r2 cos ? 2 = ( 5. 00 m ) cos ( ? 50. 0°) = 3. 21 m y2 = r2 ungodliness ? 2 = ( 5. 00 m ) ungodliness ( ? 50. 0°) = ? 3. 3 m abided on present page http://helpyoustudy. info Introduction 11 The interintervenience natant the bcareer apexs is then: ? s = ( ? x ) + ( ? y ) = (1. 29 m ? 3. 21 m ) + (1. 53 m + 3. 83 m ) = 5. 69 m 2 2 2 2 1. 40 Consider the Figure pretencen at the suitable. The Cartesian coordinates ce the bcareer apexs are: x1 = r1 cos ? 1 y1 = r1 ungodliness ? 1 x2 = r2 cos ? 2 y2 = r2 ungodliness ? 2 y (x1, y1) r1 ?s ?y y1 y2 The interintervenience natant the bcareer apexs is the prolixity of the hypotenmanifestation of the sequestesanguine trileaning and is dedicated by ? s = ( ? x ) + ( ? y ) = 2 2 q1 ( x1 ? x2 ) + ( y1 ? y2 ) 2 2 (x2, y2) r2 ? x q2 x1 x2 x or ? s = (r 2 1 cos 2 ? 1 + r22 cos 2 ? ? 2r1r2 cos ? 1 cos ? 2 ) + ( r12 ungodliness 2 ? 1 + r22 ungodliness 2 ? 2 ? 2r1r2 ungodliness ? 1 ungodliness ? 2 ) = r12 ( cos 2 ? 1 + ungodliness 2 ? 1 ) + r22 ( cos 2 ? 2 + ungodliness 2 ? 2 ) ? 2r1r2 ( cos ? 1 cos ? 2 + ungodliness ? 1 ungodliness ? 2 ) i Applying the identities cos 2 ? + ungodliness 2 ? = 1 and cos ? 1 cos ? 2 + ungodliness ? 1 ungodliness ? 2 = cos (? 1 ? ?2 ) , this sanguineuces to ? s = r12 + r22 ? 2r1r2 ( cos ? 1 cos ? 2 + ungodliness ? 1 ungodliness ? 2 ) = 1. 41 (a) r12 + r22 ? 2r1r2 cos (? 1 ? ?2 ) With a = 6. 00 m and b morals bcareer distributeys of this suitoperative trileaning having hypotenmanifestation c = 9. 00 m, the Pythagorean theorem confers the unrecognized distributey as b = c2 ? a2 = ( 9. 00 m )2 ? ( 6. 00 m )2 = 6. 1 m (c) ungodliness ? = b 6. 71 m = = 0. 746 c 9. 00 m (b) tan ? = a 6. 00 m = = 0. 894 b 6. 71 m 1. 42 From the diagram, cos ( 75. 0°) = d L Thus, d = L cos ( 75. 0°) = ( 9. 00 m ) cos ( 75. 0°) = 2. 33 m L 9 . 00 m 75. 0 d http://helpyoustudy. info 12 Chapter 1 1. 43 The enclosure of the fountain is C = 2? r , so the radius is C 15. 0 m = = 2. 39 m 2? 2? h h Thus, tan ( 55. 0°) = = which confers r 2. 39 m r= h = ( 2. 39 m ) tan ( 55. 0°) = 3. 41 m 1. 44 (a) (b) ungodliness ? = cos ? = adverse distributey so, adverse distributey = ( 3. 00 m ) ungodliness ( 30. 0° ) = 1. 50 m hypotenmanifestation nigh distributey so, nigh distributey = ( 3. 00 m ) cos ( 30. ° ) = 2 . 60 m hypotenmanifestation (b) (d) The distributey nigh to ? = 3. 00 ungodliness ? = 4. 00 = 0. 800 5. 00 1. 45 (a) (c) (e) The distributey adverse ? = 3. 00 cos ? = tan ? = 4. 00 = 0. 800 5. 00 4. 00 = 1. 33 3. 00 1. 46 Using the diagram at the suitable, the Pythagorean theorem concedes c = ( 5. 00 m ) + ( 7. 00 m ) = 8. 60 m 2 2 5. 00 m c q 7. 00 m 1. 47 From the diagram dedicated in Exaltation 1. 46 aggravate, it is beholdn that tan ? = 5. 00 = 0. 714 7. 00 and ? = tan ? 1 ( 0. 714 ) = 35. 5° 1. 48 (a) and (b) (c) Behold the Figure dedicated at the suitable. Applying the de? nition of the tangent power to the wide suitoperative trileaning compriseing the 12. ° leaning confers: y x = tan 12. 0° [1] Too, applying the de? nition of the tangent power to the inferiorer suitoperative trileaning compriseing the 14. 0° leaning confers: y = tan 14. 0° x ? 1. 00 km (d) From Equation [1] aggravate, mark that x = y tan 12. 0° [2] Substituting this development into Equation [2] confers y ? tan 12. 0° = tan 14. 0° y ? (1. 00 km ) tan 12. 0° abided on present page http://helpyoustudy. info Introduction 13 Then, solving ce the crisis of the mountain, y, concedes y= 1. 49 (1. 00 km ) tan 12. 0° tan 14. 0° tan 14. 0° ? tan 12. 0° = 1. 44 km = 1. 44 ? 10 3 m Using the draw at the suitable: w = tan 35. ° , or 100 m w = (100 m ) tan 35. 0° = 70. 0 m w 1. 50 The ? gure at the suitoperative pretences the top illustrative in the exaltation proposition. Applying the de? nition of the tangent power to the wide suitoperative trileaning compriseing the leaning ? in the Figure, sundericular succeeds y x = tan ? Too, applying the de? nition of the tangent power to the smenbore suitoperative trileaning compriseing the leaning ? confers y = tan ? x? d Solving Equation [1] ce x and substituting the development into Equation [2] concedes y = tan ? y tan ? ? d The ultimate development simpli? es to or y ? tan ? = tan ? y ? d ? tan ? y ? tan ? = y ? tan ? ? d ? tan ? ? tan ? or [2] [1]
Solving ce y: y ( tan ? ? tan ? ) = ? d ? tan ? ? tan ? y=? 1. 51 (a) d ? tan ? ? tan ? d ? tan ? ? tan ? = tan ? ? tan ? tan ? ? tan ? Dedicated that a ? F m , we keep F ? ma . Coercion-this-reason, the items of cece are those of ma, [ F ] = [ ma] = [ m][a] = M ( L T 2 ) = M L T-2 (b) L M? L [F ] = M ? 2 ? = 2 ? ? T ? T ? 1 so newton = kg ? m s2 1. 52 (a) mi ? mi ? ? 1. 609 km ? km = ? 1 ?? ? = 1. 609 h ? h ? ? 1 mi ? h mi ? mi ? ? 1. 609 km h ? km = ? 55 ?? ? = 88 h ? h ? ? 1 mi h ? h mi mi ? mi ? ? 1. 609 km h ? km ? 55 = ? 10 ?? ? = 16 h h ? h ? ? 1 mi h ? h (b) vmax = 55 (c) ?vmax = 65 http://helpyoustudy. info 14 Chapter 1 1. 3 (a) Past 1 m = 10 2 cm , then 1 m 3 = (1 m ) = (10 2 cm ) = (10 2 ) cm 3 = 10 6 cm 3, giving 3 3 3 ? 1. 0 ? 10 ? 3 kg ? 3 concretion = blindness capacity = ? ? 1. 0 m 3 ? 1. 0 cm ? ( )( ) ( ) ? 10 6 cm3 ? ? kg ? 3 = ? 1. 0 ? 10 ? 3 3 ? 1. 0 m 3 ? ? = 1. 0 ? 10 kg 3 ? cm ? ? 1m ? ( ) As a knotty regard, trmunch each of the followingcited appearances as if they were 100% steep. (b) (c) (d) 3 kg 4 cell: concretion = blindness ? capacity = ? 10 3 3 ? ? ( 0. 50 ? 10 ? 6 m ) = 5. 2 ? 10 ? 16 kg ? ? m ? 3 ? 3 4 kg 4 kidney: concretion = blindness ? capacity = ? ? ? r 3 ? = ? 10 3 3 ? ? ( 4. 0 ? 10 ? 2 m ) = 0. 27 kg ? ? ? ? m ? 3 ? 3 ? ? ?y: concretion = blindness ? olume = ( blindness ) (? r 2 h ) 2 kg = ? 10 3 3 ? ? (1. 0 ? 10 ? 3 m ) ( 4. 0 ? 10 ? 3 m ) = 1. 3 ? 10 ? 5 kg ? ? m ? ? 1. 54 Presume an mediocre of 1 can per idiosyncratic each week and a population of 300 darling. (a) calculate cans idiosyncratic ? calculate cans year = ? ? ? ( population )( weeks year ) week ? ? ? ?1 ? ? can idiosyncratic ? 8 ? ( 3 ? 10 nation ) ( 52 weeks yr ) week ? ? 2 ? 1010 cans yr , or ~10 10 cans yr (b) calculate of tons = ( gravity can )( calculate cans year ) ? oz ? ? 1 lb ? ? 1 ton ?? ? 10 can ? ? ?? 0. 5 ? ?? ?? ?? ? 2 ? 10 ? can ? ? 16 oz ? ? 2 000 lb ?? ? yr ? ?? ? 3 ? 10 5 ton yr , or ~10 5 ton yr Presumes an mediocre gravity of 0. oz of aluminum per can. 1. 55 The promise s has bulk of L, a has bulk of LT? 2, and t has bulk of T. Coercion-this-reason, the equation, s = k a m t n with k morals configurationless, has bulk of L = ( LT ? 2 ) ( T ) m n or L1T 0 = L m T n? 2 m The powers of L and T must be the identical on each distributey of the equation. Coercion-this-reason, L1 = Lm and m =1 Enjoywise, equating powers of T, we behold that n ? 2 m = 0, or n = 2 m = 2 Configurational decomcollocation canrefertelling distributeicularize the appraise of k , a configurationshort perpetual. 1. 56 (a) The admonish of ? lling in gallons per remedy is admonish = 30. 0 gal ? 1 min ? ?2 ? ? = 7. 14 ? 10 gal s 7. 0 min ? 60 s ? abided on present page http://helpyoustudy. info Introduction 15 (b) 3 1L Referablee that 1 m 3 = (10 2 cm ) = (10 6 cm 3 ) ? 3 ? 3 ? 10 cm ? = 10 3 L. Thus, ? ? admonish = 7. 14 ? 10 ? 2 (c) t= gal ? 3. 786 L ? ? 1 m 3 ? ?4 3 ? ?? ? = 2. 70 ? 10 m s s ? 1 gal ? ? 10 3 L ? ? 1h ? Vfilled 1. 00 m 3 = = 3. 70 ? 10 3 s ? ? = 1. 03 h ? 4 3 admonish 2. 70 ? 10 m s ? 3 600 s ? 1. 57 The capacity of delineate manifestationd is dedicated by V = Ah, where A is the area adept and h is the brawniness of the flake. Thus, h= V 3. 79 ? 10 ? 3 m 3 = = 1. 52 ? 10 ? 4 m = 152 ? 10 ? 6 m = 152 ? m 25. 0 m 2 A 1. 58 (a) Ce a globe, A = 4? R 2 .
In this instance, the radius of the remedy globe is twice that of the ? rst, or R2 = 2 R1. Future, A2 4? R 2 R 2 ( 2 R1 ) 2 = = 2 = = 4 2 2 A1 4? R 1 R 1 R12 2 (b) Ce a globe, the capacity is Thus, V= 4 3 ? R 3 3 V2 ( 4 3) ? R 3 R 3 ( 2 R1 ) 2 = = 2 = = 8 3 3 3 V1 ( 4 3) ? R 1 R 1 R1 1. 59 The think of the entirety interintervenience cars are driven each year is d = ( cars in manifestation ) ( interintervenience pilgrimageed per car ) = (100 ? 10 6 cars )(10 4 mi car ) = 1 ? 1012 mi At a admonish of 20 mi/gal, the fuel manifestationd per year would be V1 = d 1 ? 1012 mi = = 5 ? 1010 gal admonish1 20 mi gal If the admonish acceptiond to 25 mi gal, the annual fuel expenditure would be V2 = d 1 ? 012 mi = = 4 ? 1010 gal admonish2 25 mi gal and the fuel savings each year would be savings = V1 ? V2 = 5 ? 1010 gal ? 4 ? 1010 gal = 1 ? 1010 gal 1. 60 (a) The aggregate compensated per year would be dollars ? ? 8. 64 ? 10 4 s ? ? 365. 25 days ? 10 dollars annual aggregate = ? 1 000 ? ?? ?? ? = 3. 16 ? 10 s ? ? 1. 00 day ? ? yr yr ? ? Coercion-this-reason, it would procure (b) 10 ? 10 12 dollars = 3 ? 10 2 yr, 3. 16 ? 10 10 dollars yr or ~10 2 yr The enclosure of the Earth at the equator is C = 2? r = 2? 6. 378 ? 10 6 m = 4. 007 ? 10 7 m ( ) abided on present page http://helpyoustudy. info 16 Chapter 1 The prolixity of sundericular dollar jaw is 0. 55 m, so the prolixity of ten trillion jaws is m ? 12 12 = ? 0. 155 ? ? (10 ? 10 dollars ) = 1? 10 m. Thus, the ten trillion dollars would dollar ? ? compass the Earth 1 ? 1012 m n= = = 2 ? 10 4 , or ~10 4 periods C 4. 007 ? 10 7 m 1. 61 (a) (b) ? 365. 2 days ? ? 8. 64 ? 10 4 s ? 1 yr = (1 yr ) ? = 3. 16 ? 10 7 s ?? ? ? ? 1 day ? 1 yr ? ? ? Consider a limb of the demeanor of the Moon which has an area of 1 m2 and a profoundness of 1 m. When ? lled with meteorites, each having a bisection 10? 6 m, the calculate of meteorites ahanker each benjoin of this buffet is n= prolixity of an benjoin 1m = = 10 6 meteorite bisection 10 ? 6 m The entirety calculate of meteorites in the ? led buffet is then N = n 3 = 10 6 3 = 10 18 At the admonish of 1 meteorite per remedy, the period to ? ll the buffet is 1y ? = 3 ? 10 10 yr, or t = 1018 s = (1018 s ) ? ? ? 7 ? 3. 16 ? 10 s ? 1. 62 ~1010 yr ( ) We produce presume that, on mediocre, 1 benbore produce be past per hitter, that there produce be encircling 10 hitters per inning, a diversion has 9 innings, and the team plays 81 home diversions per opportunity. Our think of the calculate of diversion globes needed per opportunity is then calculate of globes needed = ( calculate past per hitter ) ( calculate hitters/diversion )( home diversions/year ) ?? diversions ? hitters ? ? innings ?? ? = (1 benbore per hitter ) ?? 10 ?? ? 81 ? ? ? year ? inning ? ? diversion ?? ? ?? = 7300 globes year or ~10 4 globes year 1. 63 The capacity of the Milky Way picking is knottyly ? ?d2 ? ? VG = At = ? t ? 10 21 m 4 ? 4 ? ? ( ) (10 m ) 2 19 or VG ? 10 61 m3 r If, amid the Milky Way picking, there is normally sundericular neutron bigwig in a round capacity of radius r = 3 ? 1018 m, then the galactic capacity per neutron bigwig is V1 = 3 4 3 4 ? r = ? ( 3 ? 1018 m ) = 1 ? 10 56 m 3 3 3 or V1 ? 10 56 m 3 The regulate of heap of the calculate of neutron bigwigs in the Milky Way is then n= VG 10 61 m 3 ? V1 10 56 m 3 or n ? 10 5 neutron bigwigs http://helpyoustudy. info 2 Disturbance in Sundericular Configuration
QUICK QUIZZES 1. 2. (a) (a) 200 yd (b) 0 (c) 0 Faithless. The car may be lateing down, so that the inclination of its succor is adverse the inclination of its swiftness. Penny. If the swiftness is in the inclination clarified as disclaiming, a despotic succor causes a diminish in accelerate. Penny. Ce an accelerating keep-ajot to bung at entire, the swiftness and succor must keep adverse indications, so that the acceleadmonish is decreasing. If this is the instance, the keep-ajot produce refertelling attributtelling attributtelling attributtelling attributtelling attributablewithstanding purpose to interim. If the succor recrement perpetual, however, the keep-ajot must commence to instigate intermittently, adverse to the inclination of its cemer swiftness.
If the keep-ajot purposes to interim and then stays at interim, the succor has bepurpose naught at the avail the disturbance bungs. This is the instance ce a braking car—the succor is disclaiming and goes to naught as the car purposes to interim. (b) (c) 3. The swiftness-vs. -period graph (a) has a perpetual prosper, indicating a perpetual succor, which is represented by the succor-vs. -period graph (e). Graph (b) represents an appearance whose acceleadmonish regularly acceptions, and does so at an intermissionraintforever increasing admonish. Thus, the succor must be increasing, and the succor-vs. -period graph that best indicates this comportment is (d).
Graph (c) depicts an appearance which ? rst has a swiftness that acceptions at a perpetual admonish, which resources that the appearance’s succor is perpetual. The disturbance then qualifys to sundericular at perpetual accelerate, indicating that the succor of the appearance beseems naught. Thus, the best pactivity to this top is graph (f). 4. Exquisite (b). According to graph b, there are some moments in period when the appearance is coincidently at bcareer disagreeent x-coordinates. This is physically unusable. (a) The cerulean graph of Figure 2. 14b best pretences the abortion’s collocation as a power of period. As beholdn in Figure 2. 4a, the interintervenience the abortion has pilgrimageed grows at an increasing admonish ce resemblely three period interims, grows at a equtelling admonish ce encircling lewd period interims, and then grows at a powershort admonish ce the ultimate bcareer interims. The sanguine graph of Figure 2. 14c best illustrates the acceleadmonish (interintervenience pilgrimageed per period interim) of the abortion as a power of period. It pretences the abortion produceing acceleadmonish ce resemblely three period interims, melting at perpetual acceleadmonish ce encircling lewd period interims, then lateing to interim during the ultimate bcareer interims. 5. (b) 17 http://helpyoustudy. info 18 Chapter 2 (c) The unpractised graph of Figure 2. 4d best pretences the abortion’s succor as a power of period. The abortion produces swiftness (despotic succor) ce resemblely three period interims, instigates at perpetual swiftness (naught succor) ce encircling lewd period interims, and then loses swiftness (disclaiming succor) ce knottyly the ultimate bcareer period interims. 6. Exquisite (e). The succor of the benbore recrement perpetual suitableness it is in the activity. The heap of its succor is the operating-fenbore succor, g = 9. 80 m/s2. Exquisite (c). As it pilgrimages upward, its acceleadmonish diminishs by 9. 80 m/s during each remedy of its disturbance. When it reaches the peak of its disturbance, its acceleadmonish beseems naught.
As the benbore instigates downward, its acceleadmonish acceptions by 9. 80 m/s each remedy. Exquisites (a) and (f). The ? rst jumper produce regularly be melting with a surpassing swiftness than the remedy. Thus, in a dedicated period interim, the ? rst jumper covers aggravate interintervenience than the remedy, and the disengagement interintervenience natant them acceptions. At any dedicated moment of period, the velocities of the jumpers are de? nitely disagreeent, consequently sundericular had a chief bigwigt. In a period interim following this moment, however, each jumper acceptions his or her swiftness by the identical aggregate, consequently they keep the identical succor. Thus, the disagreeence in velocities stays the identical. . 8. ANSWERS TO MULTIPLE CHOICE QUESTIONS 1. Once the arrow has left the bow, it has a perpetual downward succor resembling to the operatingfenbore succor, g. Taking upward as the despotic inclination, the departed period exactd ce the swiftness to qualify from an modeblame appraise of 15. 0 m s upward ( v0 = +15. 0 m s ) to a appraise of 8. 00 m s downward ( v f = ? 8. 00 m s ) is dedicated by ? t = ? v v f ? v0 ? 8. 00 m s ? ( +15. 0 m s ) = = = 2. 35 s a ? g ? 9. 80 m s 2 Thus, the improve exquisite is (d). 2. In Figure MCQ2. 2, there are ? ve interveniences separating nigh grease drops, and these interveniences p a interintervenience of ? x = 600 meters.
Past the drops appear intermissionraintconsummate 5. 0 s, the period p of each intervenience is 5. 0 s and the entirety period interim pretencen in the ? gure is ? t = 5 ( 5. 0 s ) = 25 s. The mediocre acceleadmonish of the car is then v= ? x 600 m = = 24 m s ? t 25 s making (b) the improve exquisite. 3. The commencening of the equations of kinematics ce an appearance melting in sundericular configuration (Equations 2. 6 thknotty 2. 10 in the textbook) was infamousd on the presumption that the appearance had a perpetual succor. Thus, (b) is the improve apology. An appearance having perpetual succor would keep perpetual swiftness barely if that succor had a appraise of naught, so (a) is refertelling a compulsory mood.
The acceleadmonish (heap of the swiftness) produce acception in period barely in instances when the swiftness is in the identical inclination as the perpetual succor, so (c) is refertelling a improve vindication. An appearance inconsummate correct upward into the activity has a perpetual succor. Yet its collocation (altitude) does refertelling regularly acception in period (it refertelling attributtelling attributtelling attributtelling attributtelling attributablewithstanding bigwigts to fenbore purpose downward) nor is its swiftness regularly directed downward (the inclination of the perpetual succor). Thus, neither (d) nor (e) can be improve. http://helpyoustudy. info Disturbance in Sundericular Configuration 19 4. The bowling molehill has a perpetual downward succor ( a = ? g = ? 9. 80 m s 2 ) suitableness in ? ght. The swiftness of the molehill is directed upward on the upward keep-akeep-adistribute of its ? ight and is directed downward as it lapses purpose inlaterality the juggler’s artisan. Thus, barely (d) is a penny proposition. The modeblame swiftness of the car is v0 = 0 and the swiftness at period t is v. The perpetual succor is coercion-this-reason dedicated by a = ? v ? t = ( v ? v0 ) t = ( v ? 0 ) t = v t and the mediocre swiftness of the car is v = ( v + v0 ) 2 = ( v + 0 ) 2 = v 2. The interintervenience pilgrimageed in period t is ? x = vt = vt 2. In the sundericular instance where a = 0 ( and future v = v0 = 0 ) , we behold that propositions (a), (b), (c), and (d) are enbore improve. However, in the open instance ( a ? , and future v ? 0 ), barely propositions (b) and (c) are penny. Prostanding (e) is refertelling penny in either instance. The disturbance of the boat is very common to that of a appearance thrown correct upward into the activity. In twain instances, the appearance has a perpetual succor which is directed adverse to the inclination of the modeblame swiftness. Sound as the appearance thrown upward lates down and bungs availarily precedently it bigwigts accelerateing up as it lapses purpose downward, the boat produce abide to instigate northward ce some period, lateing once until it purposes to a availary bung. It produce then bigwigt to instigate in the southward inclination, produceing acceleadmonish as it goes.
The improve apology is (c). In a collocation versus period graph, the swiftness of the appearance at any apex in period is the prosper of the outoutthread tangent to the graph at that moment in period. The acceleadmonish of the keep-ajot at this apex in period is solely the heap (or despotic appraise) of the swiftness at this moment in period. The misconstruction appearring during a period interim is resembling to the disagreeence in x-coordinates at the ? nal and modeblame periods of the interim ? x = x t f ? x ti . 5. 6. 7. ( ) The mediocre swiftness during a period interim is the prosper of the correct outoutthread connecting the apexs on the flexion identical to the modeblame and ? al periods of the interim ? v = ? x ? t = ( x f ? xi ) ( t f ? ti ) ? . Thus, we behold how the quantities in exquisites (a), (e), (c), and (d) ? ? can enbore be succeeded from the graph. Barely the succor, exquisite (b), canrefertelling be succeeded from the collocation versus period graph. 8. From ? x = v0 t + 1 at 2, the interintervenience pilgrimageed in period t, bigwigting from interim ( v0 = 0 ) with perpetual 2 succor a, is ? x = 1 at 2 . Thus, the proportion of the interspaces pilgrimageed in bcareer sundericular trials, sundericular 2 of continuance t1 = 6 s and the remedy of continuance t 2 = 2 s, is 2 2 ? x2 1 at 2 ? t 2 ? ? 2 s ? 1 2 = 1 2 =? ? =? ? = ? x1 2 at1 ? 1 ? ? 6 s ? 9 and the improve apology is (c). 2 9. The interintervenience an appearance melting at a conformtelling acceleadmonish of v = 8. 5 m s produce pilgreffigy during a period interim of ? t = 1 1 000 s = 1. 0 ? 10 ? 3 s is dedicated by ? x = v ( ? t ) = (8. 5 m s ) (1. 0 ? 10 ? 3 s ) = 8. 5 ? 10 ? 3 m = 8. 5 mm so the barely improve apology to this interrogation is exquisite (d). 10. Once either benbore has left the student’s artisan, it is a voluntarily lapseing collectiveness with a perpetual succor a = ? g (taking upward as despotic). Coercion-this-reason, exquisite (e) canrefertelling be penny. The modeblame velocities of the sanguine and cerulean globes are dedicated by viR = + v0 and viB = ? 0 , respectively. The swiftness of either benbore when it has a misconstruction from the propel apex of ? y = ? h (where h is the crisis of the fabric) is root from v 2 = vi2 + 2a ( ? y ) as follows: 2 vR = ? viR + 2a ( ? y ) R = ? ( + v0 ) 2 + 2 ( ? g ) ( ? h ) = ? 2 v0 + 2 gh http://helpyoustudy. info 20 Chapter 2 and 2 vB = ? viB + 2a ( ? y ) B = ? ( ? v0 ) 2 + 2 ( ? g ) ( ? h ) = ? 2 v0 + 2 gh Referablee that the disclaiming indication was clarified ce the natural in twain instances past each benbore is melting in the downward inclination presently precedently it reaches the reason.
From this, we behold that exquisite (c) is penny. Too, the accelerates of the bcareer globes sound precedently hitting the reason are 2 2 2 2 vR = ? v0 + 2 gh = v0 + 2 gh > v0 and vB = ? v0 + 2 gh = v0 + 2 gh > v0 Coercion-this-reason, vR = vB , so twain exquisites (a) and (b) are faithless. However, we behold that twain ? nal accelerates surpass the modeblame acceleadmonish and exquisite (d) is penny. The improve apology to this interrogation is then (c) and (d). 11. At reason roll, the misconstruction of the buffet from its propel apex is ? y = ? h , where h is the 2 crisis of the aspire and upward has been clarified as the despotic inclination.
From v 2 = vo + 2a ( ? y ) , the acceleadmonish of the buffet sound precedently hitting the reason is root to be 2 2 v = ± v0 + 2a ( ? y ) = v0 + 2 ( ? g ) ( ? h ) = (12 m s )2 + 2 ( 9. 8 m s2 ) ( 40. 0 m ) = 30 m s Exquisite (b) is coercion-this-reason the improve vindication to this interrogation. 12. Once the benbore has left the thrower’s artisan, it is a voluntarily lapseing collectiveness with a perpetual, non-zero, succor of a = ? g . Past the succor of the benbore is refertelling naught at any apex on its trajectory, exquisites (a) thknotty (d) are enbore faithshort and the improve vindication is (e). ANSWERS TO EVEN NUMBERED CONCEPTUAL QUESTIONS . Yes. The keep-ajot may bung at some moment, yet tranquil keep an succor, as when a benbore thrown correct up reaches its apex crisis. (a) (b) 6. (a) No. They can be manifestationd barely when the succor is perpetual. Yes. Naught is a perpetual. In Figure (c), the effigys are farther akeep-adistribute ce each successive period interim. The appearance is melting inlaterality the suitoperative and accelerateing up. This resources that the succor is despotic in Figure (c). In Figure (a), the ? rst lewd effigys pretence an increasing interintervenience pilgrimageed each period interim and coercion-this-reason a despotic succor.
However, following the lewdth effigy, the spacing is decreasing, pretenceing that the appearance is now lateing down (or has disclaiming succor). In Figure (b), the effigys are resemblingly intervenienced, pretenceing that the appearance instigated the identical interintervenience in each period interim. Future, the swiftness is perpetual in Figure (b). At the apex crisis, the benbore is availarily at interim (i. e. , has naught swiftness). The succor recrement perpetual, with heap resembling to the operating-fenbore succor g and directed downward. Thus, conformtelling though the swiftness is availarily naught, it abides to qualify, and the benbore produce commence to produce acceleadmonish in the downward inclination.
The succor of the benbore recrement perpetual in heap and inclination throughextinguished the globe’s operating ? ight, from the moment it leaves the artisan until the moment sound precedently it strikes the 4. (b) (c) 8. (a) (b) http://helpyoustudy. info Disturbance in Sundericular Configuration 21 reason. The succor is directed downward and has a heap resembling to the operatingfenbore succor g. 10. (a) Successive effigys on the ? lm produce be disjoined by a perpetual interintervenience if the benbore has perpetual swiftness. Bigwigting at the suitable-most effigy, the effigys produce be procureting closer concomitantly as sundericular instigates inlaterality the left.
Starting at the suitable-most effigy, the effigys produce be procureting farther akeep-adistribute as sundericular instigates inlaterality the left. As sundericular instigates from left to suitable, the globes produce ? rst procure farther akeep-adistribute in each successive effigy, then closer concomitantly when the benbore commences to late down. (b) (c) (d) ANSWERS TO EVEN NUMBERED PROBLEMS 2. 4. 6. (a) (a) (a) (d) 8. (a) (d) 10. 12. (a) (a) (d) 14. 16. (a) 2 ? 10 4 mi 10. 04 m s 5. 00 m s ? 3. 33 m s +4. 0 m s 0 2. 3 min L t1 2 L ( t1 + t 2 ) 1. 3 ? 10 2 s (b) 13 m (b) (b) 64 mi ? L t 2 (c) 0 (b) (b) (b) (e) (b) ? x 2 RE = 2. 4 7. 042 m s 1. 25 m s 0 ? 0. 50 m s (c) ? 1. 0 m s (c) ? 2. 50 m s a) The luxuriance runner’s acceleadmonish must be senior than that of the chief, and the chief’s interintervenience from the ? nish outoutthread must be grmunch ample to confer the luxuriance runner period to create up the de? cient interspace. (b) t = d ( v1 ? v2 ) (c) d2 = v2 d ( v1 ? v2 ) 18. (a) Some reasons apexs that can be manifestationd to contrive the graph are as dedicated under: x (m) t (s) (b) (c) 5. 75 1. 00 16. 0 2. 00 35. 3 3. 00 68. 0 4. 00 119 5. 00 192 6. 00 41. 0 m s , 41. 0 m s , 41. 0 m s 17. 0 m s , plenteous inferiorer than the momentaneous swiftness at t = 4. 00 s l http://helpyoustudy. info 22 Chapter 2 20. 22. 24. (a) 20. 0 m s , 5. 00 m s (b) 263 m 0. 91 s (i) (a) (ii) (a) 0 0 (b) (b) 1. 6 m s 2 1. 6 m s 2 500 x (m) (c) (c) 0. 80 m s 2 0 26. The flexions anastomose at t = 16. 9 s. car police conductor 250 0 0 4. 00 8. 00 12. 0 16. 0 20. 0 t (s) 28. 30. a = 2. 74 ? 10 5 m s 2 = ( 2. 79 ? 10 4 ) g (a) (b) (e) 32. (a) (d) 34. 36. 38. 40. (a) (a) (a) (a) (c) 42. 44. 46. 48. 95 m 29. 1 s 1. 79 s v 2 = vi2 + 2a ( ? x ) f 8. 00 s 13. 5 m 22. 5 m 20. 0 s 5. 51 km 107 m v = a1t1 (c) a = ( v 2 ? vi2 ) 2 ( ? x ) f (d) 1. 25 m s 2 (b) 13. 5 m (c) 13. 5 m (b) (b) (b) (b) No, it canrefertelling establish safely on the 0. 800 km runway. 20. 8 m s, 41. 6 m s, 20. 8 m s, 38. 7 m s 1. 49 m s 2 ? = 1 a1t12 2 2 ? xentirety = 1 a1t12 + a1t1t 2 + 1 a2 t 2 2 2 (a) Yes. (b) vtop = 3. 69 m s (c) ?v downward = 2. 39 m s (d) No, ? v upward = 3. 71 m s. The bcareer buffets keep the identical succor, yet the buffet thrown downward has a surpassing mediocre acceleadmonish natant the bcareer rolls, and is dissipated aggravate a inferiorer period interim. http://helpyoustudy. info Disturbance in Sundericular Configuration 23 50. 52. (a) (a) (c) 21. 1 m s v = ? v0 ? gt = v0 + gt v = v0 ? gt , d = 1 gt 2 2 29. 4 m s ? 202 m s 2 4. 53 s vi = h t + gt 2 (b) (b) 19. 6 m d = 1 gt 2 2 (c) 18. 1 m s, 19. 6 m 54. 56. 58. 60. 62. 64. (a) (a) (a) (a) (b) (b) (b) (b) 44. 1 m 198 m 14. m s v = h t ? gt 2 Behold Disconnections Section ce Disturbance Diagrams. Yes. The narrowness succor needed to consummate the 1 mile interintervenience in the entireotted period is amin = 0. 032 m s 2 , considerably short than what she is capoperative of submissive. (a) (c) y1 = h ? v0 t ? 1 gt 2 , y2 = h + v0 t ? 1 gt 2 2 2 2 v1 f = v2 f = ? v0 + 2 gh (d) 66. (b) t 2 ? t1 = 2 v0 g y2 ? y1 = 2 v0 t as hanker as twain globes are tranquil in the activity. 68. 70. 3. 10 m s (a) (c) 3. 00 s (b) v0 ,2 = ? 15. 2 m s v1 = ? 31. 4 m s, v2 = ? 34. 8 m s 2. 2 s barely if succor = 0 (b) (b) ? 21 m s Yes, ce enbore modeblame velocities and succors. 72. 74. (a) (a)
PROBLEM SOLUTIONS 2. 1 We presume that you are resemblely 2 m tenbore and that the firmness cessationraintce pilgrimages at conformtelling accelerate. The departed period is then ? t = 2. 2 (a) 2m ? x = = 2 ? 10 ? 2 s = 0. 02 s v 100 m s At perpetual accelerate, c = 3 ? 108 m s, the interintervenience inconsidertelling pilgrimages in 0. 1 s is ? x = c ( ? t ) = ( 3 ? 108 m s ) ( 0. 1 s ) ? 1 mi ? ? 1 km ? 4 = ( 3 ? 10 7 m ) ? ? = 2 ? 10 mi ?? 3 ? 1. 609 km ? ? 10 m ? (b) Comparing the development of keep-akeep-adistribute (a) to the bisection of the Earth, DE, we ? nd 3. 0 ? 10 7 m ? x ? x = = ? 2. 4 DE 2 RE 2 ( 6. 38 ? 10 6 m ) ( with RE = Earth’s radius ) http://helpyoustudy. info 24 Chapter 2 2. 3
Distances pilgrimageed natant pairs of cities are ? x1 = v1 ( ? t1 ) = (80. 0 km h ) ( 0. 500 h ) = 40. 0 km ? x2 = v2 ( ? t 2 ) = (100 km h ) ( 0. 200 h ) = 20. 0 km ? x3 = v3 ( ? t3 ) = ( 40. 0 km h ) ( 0. 750 h ) = 30. 0 km Thus, the entirety interintervenience pilgrimageed is ? x = ( 40. 0 + 20. 0 + 30. 0 ) km = 90. 0 km, and the departed period is ? t = 0. 500 h + 0. 200 h + 0. 750 h + 0. 250 h = 1. 70 h. (a) (b) v= ? x 90. 0 km = = 52. 9 km h ? t 1. 70 h ?x = 90. 0 km (behold aggravate) v= v= ? x 2. 000 ? 10 2 m = = 10. 04 m s ? t 19. 92 s 2. 4 (a) (b) 2. 5 (a) ?x 1. 000 mi ? 1. 609 km ? ? 10 3 m ? = ? ?? ? = 7. 042 m s ? t 228. 5 s ? 1 mi ? 1 km ? Boat A exacts 1. 0 h to perverse the lake and 1. 0 h to render, entirety period 2. 0 h. Boat B exacts 2. 0 h to perverse the lake at which period the career is aggravate. Boat A wins, morals 60 km achief of B when the career purposes. Mediocre swiftness is the entoil misconstruction of the boat entireotd by the entirety departed period. The engaging boat is purpose where it bigwigted, its misconstruction thus morals naught, concedeing an mediocre swiftness of naught . (b) 2. 6 The mediocre swiftness aggravate any period interim is ? x x f ? xi = ? t t f ? ti ? x 10. 0 m ? 0 v= = = 5. 00 m s ? t 2. 00 s ? 0 v= (a) (b) (c) (d) (e) v= v= v= v= ? x 5. 00 m ? 0 = = 1. 25 m s ? 4. 00 s ? 0 ? x 5. 00 m ? 10. 0 m = = ? 2. 50 m s ? t 4. 00 s ? 2. 00 s ? x ? 5. 00 m ? 5. 00 m = = ? 3. 33 m s ? t 7. 00 s ? 4. 00 s 0? 0 ? x x2 ? x1 = = = 0 ? t t 2 ? t1 8. 00 s ? 0 2. 7 (a) (b) 1h ? Misconstruction = ? x = (85. 0 km h ) ( 35. 0 min ) ? ? ? + 130 km = 180 km ? 60. 0 min ? 1h ? The entirety departed period is ? t = ( 35. 0 min + 15. 0 min ) ? ? ? + 2. 00 h = 2. 83 h ? 60. 0 min ? so, v= ? x 180 km = = 63. 6 km h ? t 2. 84 h http://helpyoustudy. info Disturbance in Sundericular Configuration 25 2. 8 The mediocre swiftness aggravate any period interim is ? x x f ? xi = ? t t f ? ti ? x 4. 0 m ? 0 v= = = + 4. 0 m s ? t 1. 0 s ? 0 ? ? 2 . 0 m ? 0 v= = = ? 0. 50 m s ? t 4. 0 s ? 0 v= (a) (b) (c) (d) v= v= ? x 0 ? 4. 0 m = = ? 1. 0 m s ? t 5. 0 s ? 1. 0 s ? x 0? 0 = = 0 ? t 5. 0 s ? 0 2. 9 The flatten bigwigts from interim ( v0 = 0 ) and maintains a perpetual succor of a = +1. 3 m s 2 . Thus, we ? nd the interintervenience it produce pilgreffigy precedently reaching the exactd procureextempore acceleadmonish ( v = 75 m s ) , from 2 v 2 = v0 + 2a ( ? x ) , as ? x = 2 v 2 ? v0 ( 75 m s ) ? 0 = = 2. 2 ? 10 3 m = 2. 2 km 2 2a 2 (1. 3 m s ) 2 Past this interintervenience is short than the prolixity of the runway, the flatten procures extempore safely. 2. 10 (a) The period ce a car to create the skip is t = cars to omplete the identical 10 mile skip is ? t = t1 ? t 2 = (b) ? x ? x ? 10 mi 10 mi ? ? 60 min ? ? =? ? ? = 2. 3 min ?? v1 v2 ? 55 mi h 70 mi h ? ? 1 h ? ?x . Thus, the disagreeence in the periods ce the bcareer v When the faster car has a 15. 0 min control, it is achief by a interintervenience resembling to that pilgrimageed by the lateer car in a period of 15. 0 min. This interintervenience is dedicated by ? x1 = v1 ( ? t ) = ( 55 mi h ) (15 min ). The faster car pulls achief of the lateer car at a admonish of vrelative = 70 mi h ? 55 mi h = 15 mi h Thus, the period exactd ce it to procure interintervenience ? x1 achief is ? t = ? x1 = vrelative ( 55 mi h ) (15 min ) 15. 0 mi h = 55 min
Finally, the interintervenience the faster car has pilgrimageed during this period is ? x2 = v2 ( ? t ) = 2. 11 (a) ( 70 mi h ) ( 55 min ) ? ? 1h ? ? = 64 mi ? 60 min ? From v 2 = vi2 + 2a ( ? x ) , with vi = 0 , v f = 72 km h , and ? x = 45 m, the succor of the f cheetah is root to be ?? km ? ? 10 3 m ? ? 1 h ?? ?? 72 ?? ? 0 ?? ?? h ? ? 1 km ? ? 3 600 s ?? v 2 ? vi2 ?? f a= = = 4. 4 m s 2 2 ( ? x ) 2 ( 45 m ) abided on present page 2 http://helpyoustudy. info 26 Chapter 2 (b) The cheetah’s misconstruction 3. 5 s following bigwigting from interim is 1 1 2 ? x = vi t + at 2 = 0 + ( 4. 4 m s 2 ) ( 3. 5 s ) = 27 m 2 2 2. 12 (a) (b) (c) (d) 1 = v2 = ( ? x )1 + L = = + L t1 ( ? t )1 t1 ( ? x )2 ? L = = ? L t2 ( ? t )2 t 2 ( ? x ) entirety ( ? x )1 + ( ? x )2 + L ? L 0 = = = 0 = t1 + t 2 t1 + t 2 t1 + t 2 ( ? t ) entirety +L + ? L entirety interintervenience pilgrimageed ( ? x )1 + ( ? x )2 2L = = = ( ave. acceleadmonish )skip = t1 + t 2 t1 + t 2 t1 + t 2 ( ? t ) entirety ventirety = The entirety period ce the skip is t entirety = t1 + 22 . 0 min = t1 + 0. 367 h , where t1 is the period departed pilgrimageing at v1 = 89. 5 km h. Thus, the interintervenience pilgrimageed is ? x = v1 t1 = vt entirety, which confers 2. 13 (a) (89. 5 km h ) t1 = ( 77. 8 km h ) ( t1 + 0. 367 h ) = ( 77. 8 km h ) t1 + 28. 5 km or, (89. 5 km h ? 77. km h ) t1 = 28. 5 km From which, t1 = 2 . 44 h ce a entirety period of t entirety = t1 + 0. 367 h = 2. 81 h (b) The interintervenience pilgrimageed during the skip is ? x = v1 t1 = vt entirety, giving ? x = v tentirety = ( 77. 8 km h ) ( 2. 81 h ) = 219 km 2. 14 (a) At the purpose of the career, the tortoise has been melting ce period t and the valutelling ce a period t ? 2 . 0 min = t ? 120 s. The acceleadmonish of the tortoise is vt = 0. 100 m s, and the acceleadmonish of the valutelling is vh = 20 vt = 2 . 0 m s. The tortoise pilgrimages interintervenience xt, which is 0. 20 m wider than the interintervenience xh pilgrimageed by the valuable. Future, xt = xh + 0. 20 m which beseems or vt t = vh ( t ? 120 s ) + 0. 0 m ( 0. 100 m s ) t = ( 2 . 0 m s ) ( t ? 120 s ) + 0. 20 m t = 1. 3 ? 10 2 s This confers the period of the career as (b) 2. 15 xt = vt t = ( 0. 100 m s ) (1. 3 ? 10 2 s ) = 13 m The apex entireowed period to consummate the skip is t entirety = entirety interintervenience 1600 m ? 1 km h ? = ? ? = 23. 0 s exactd mediocre acceleadmonish 250 km h ? 0. 278 m s ? The period departed in the ? rst half of the skip is t1 = half interintervenience 800 m ? 1 km h ? = ? ? = 12 . 5 s v1 230 km h ? 0. 278 m s ? abided on present page http://helpyoustudy. info Disturbance in Sundericular Configuration 27 Thus, the apex period that can be departed on the remedy half of the skip is t 2 = t entirety ? 1 = 23. 0 s ? 12 . 5 s = 10. 5 s and the exactd mediocre acceleadmonish on the remedy half is v2 = 2. 16 (a) ? 1 km h ? half interintervenience 800 m = = 76. 2 m s ? ? = 274 km h t2 10. 5 s ? 0. 278 m s ? In regulate ce the luxuriance athlete to be operative to seize the chief, his acceleadmonish (v1) must be senior than that of the controling athlete (v2), and the interintervenience natant the controling athlete and the ? nish outoutthread must be grmunch ample to confer the luxuriance athlete suf? cient period to create up the de? cient interspace, d. During a period t the controling athlete produce pilgreffigy a interintervenience d2 = v2 t and the luxuriance athlete produce pilgreffigy a interintervenience d1 = v1t .
Barely when d1 = d2 + d (where d is the modeblame interintervenience the luxuriance athlete was aback the chief) produce the luxuriance athlete keep caught the chief. Requiring that this mood be satis? ed confers the departed period exactd ce the remedy athlete to aggravateprocure the ? rst: d1 = d2 + d giving or v1t = v2 t + d or t = d ( v1 ? v2 ) (b) v1t ? v2 t = d (c) In regulate ce the luxuriance athlete to be operative to at inferiointerim retain ce ? rst establish, the modeblame interintervenience D natant the chief and the ? nish outoutthread must be senior than or resembling to the interintervenience the chief can pilgreffigy in the period t adapted aggravate (i. e. , the period exactd to aggravateprocure the chief).
That is, we must exact that D ? d2 = v2 t = v2 ? d ( v1 ? v2 ) ? ? ? or D? v2 d v1 ? v2 2. 17 The momentaneous swiftness at any period is the prosper of the x vs. t graph at that period. We calculate this prosper by using bcareer apexs on a correct limb of the flexion, sundericular apex on each distributey of the apex of profit. (a) (b) (c) (d) vt=1. 00 s = vt=3. 00 s = 10. 0 m ? 0 = 5. 00 m s 2 . 00 s ? 0 ( 5. 00 ? 10. 0 ) m = ? 2 . 50 m s ( 4. 00 ? 2 . 00 ) s ( 5. 00 ? 5. 00 ) m vt=4. 50 s = = 0 ( 5. 00 ? 4. 00 ) s 0 ? ( ? 5. 00 m ) vt=7. 50 s = = 5. 00 m s (8. 00 ? 7. 00 ) s http://helpyoustudy. info 28 Chapter 2 2. 18

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