90 m s 2 546 s 730 m 2 44 chapter 2 c at

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Unformatted text preview: 2 t 2 = 4.00 s . ( ) Thus, the difference in the time of flight for the two balls is ∆t = t 2 − t1 = ( 4.00 − 1.00) s= 3.00 s . (b) When the balls strike the ground, their velocities are: ( ) ( ) v 1 f = v 1i − gt1 = −14.7 m s − 9.80 m s 2 (1.00 s ) = − 24.5 m s , and v 2 f = v 2i − gt 2 = + 14.7 m s − 9.80 m s 2 ( 4.00 s ) = − 24.5 m s . (c) At t = 0.800 s, the displacement of each ball from the balcony is: ( ) ( ) 1 2 ∆y 1 = y1 − 0 = v1i t − gt 2 = ( −14.7 m s ) ( 0.800 s ) − 4.90 m s 2 ( 0.800 s ) , 2 1 2 ∆y 2 = y 2 − 0 = v 2i t − gt 2 = ( +14.7 m s ) ( 0.800 s ) − 4.90 m s 2 ( 0.800 s ) . 2 These yield y 1 = −14.9 m a n d y 2 = + 8.62 m . Therefore the distance separating the two balls at this time is d = y 2 − y1 = 8.62 m − ( −14.9 m ) = 23.5 m 43 CHAPTER 2.60 2 We do not know either the initial velocity nor the final velocity (i.e., velocity just before impact) for the truck. What we do know is that the truck skids 62.4 m in 4.20 s while accelerating at −5.60 m s 2 . ⎛ v f + vi ⎞ We have v f = v i + at and ∆x = vt = ⎜ ⎟ t . Applied to the motion of the truck, these ⎝2⎠ yield ( ) (1) 2 ( ∆x ) 2 ( 62.4 m ) = = 29.7 m s t 4.20 s (2) v f − v i = −5.60 m s 2 ( 4.20 s ) = −23.5 m s , v f − v i = at or and v f + vi = Adding equations (1) and (2) gives the velocity at moment of impact as 2v f = ( −23.5 + 29.7 ) m s , or v f = 3.10 m s . 2.61 When Kathy has been moving for t seconds, Stan’s elapsed time is t + 1.00 s . At this time, the displacements of the two cars are 1 2 ( ∆x ) Kathy = v iK t + aK t 2 = 0 + and ( ) 1 4.90 m s 2 t 2 , 2 1 2 ( ∆x )Stan = v iS t + aS ( t + 1.00 s ) 2 = 0 + ( ) 1 2 3.50 m s 2 ( t + 1.00 s ) . 2 (a) When Kathy overtakes Stan, ( ∆x ) Kat hy = ( ∆x )Stan , or ( 4.90 m s ) t = ( 3.50 m s ) ( t + 1.00 s) 2 2 2 2 which gives the time as t = 5.46 s . (b) Kathy’s displacement at this time is ( ∆x ) Kathy = ( ) 1 2 4.90 m s 2 ( 5.46 s ) = 73.0 m . 2 44 CHAPTER 2 (c) At this time, the velocities of the two cars are (v ) Kat hy () St an f an...
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