00 s similarly applying this relation to the motion

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Unformatted text preview: m ) 2 5 2 = -4.90 × 10 m s . (b) The average velocity as the front of the bullet passes through the board is v f + vi v board = = 350 m s and the total time of contact with the board is 2 t= ( ∆x )board Lbullet v board + vf = 0.100 m 0.0200 m + = 3.57 × 10−4 s 350 m s 280 m s (c) From v 2 = v i2 + 2 a( ∆x ) , with v f = 0 , gives the required thickness as f ∆x = v 2 − v i2 f 2a = ( 0 − ( 420 m s ) 2 2 −4.90 × 105 m s 2 ) = 0.180 m . 41 CHAPTER 2.57 2 The falling ball moves a distance of (15 m − h) before they meet, where h is the height 1 above the ground where they meet. Apply ∆y = v i t + at 2 , with a = − g to obtain 2 1 1 − (15 m − h) = 0 − gt 2 , or h = 15 m − gt 2 . 2 2 1 1 Applying ∆y = v i t + at 2 to the rising ball gives h = ( 25 m s ) t − gt 2 . 2 2 Combining equations (1) and (2) gives t = 2.58 (1) (2) 15 m = 0.60 s . 25 m s The distance required to stop the car after the brakes are applied is 2 ( ∆x ) stop ⎡ mi ⎛ 1.47 ft s ⎞ ⎤ 0 − ⎢ 35.0 ⎥ 2 2 h ⎜ 1 mi h ⎟ ⎦ v f − vi ⎝ ⎠ ⎣ = = = 147 ft . 2a 2 −9.00 ft s 2 ( ) Thus, if the deer is not to be hit, the maximum distance the car can travel before the brakes are applied is given by ( ∆x )before = 200 ft − ( ∆x ) stop = 200 ft − 147 ft = 53.0 ft . Before the brakes are applied, the constant speed of the car is 35.0 mi/h. Thus, the time required for it to travel 53.0 ft, and hence the maximum allowed reaction time, is ( tr )max = ( ∆x )before vi = 53.0 ft ⎡ mi ⎛ 1.47 ft s ⎞ ⎤ ⎢35.0 ⎥ h ⎜ 1 mi h ⎟ ⎦ ⎝ ⎠ ⎣ 42 = 1.03 s . CHAPTER 2.59 2 (a) When either ball reaches the ground, its net displacement is ∆y = −19.6 m . 1 Applying ∆y = v i t + at 2 to the motion of the first ball gives 2 1 2 −19.6 m = ( −14.7 m s ) t1 + −9.80 m s 2 t1 which has a positive solution of 2 t1 = 1.00 s . ( ) Similarly, applying this relation to the motion of the second ball gives 1 2 −19.6 m = ( +14.7 m s ) t 2 + −9.80 m s 2 t 2 which has a single positive solution of...
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This note was uploaded on 03/03/2010 for the course PHY P221 taught by Professor Dr.ha during the Spring '05 term at Indiana University South Bend.

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