0 m s vi 150 s t 2 or v i 100 m s u p w a r d

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Unformatted text preview: m . The maximum height above ground that the rocket reaches is then given by hmax = 150 m + 158 m = 308 m . (b) The total time of the upward motion of the rocket is the sum of two intervals. The first is the time for the rocket to go from v i = 50.0 m s at the ground to a velocity of v f = 55.7 m s at an altitude of 150 m. This time is given by t1 = ( ∆y )1 v1 = 2 (150 m ) = 2.84 s . ( 55.7 + 50.0) m s The second interval is the time to rise 158 m starting with v i = 55.7 m s and ending with v f = 0 . This time is t1 = ( ∆y )2 v2 = 2 (158 m ) = 5.67 s . 0+55.7 m s The total time of the upward flight is then t up = t1 + t 2 = ( 2 .84 + 5.67 ) s = 8.51 s . 38 CHAPTER 2 (c) The time for the rocket to fall 308 m back to the ground, with v i = 0 and acceleration 1 a = − g = −9.80 m s 2 , is found from ∆y = v i t + at 2 as 2 t down = 2 ( ∆y ) a = 2 ( − 308 m ) − 9.80 m s 2 = 7.93 s , so the total time of the flight is t flight = t up + t down = ( 8.51 + 7.93) s = 16.4 s . 2.50 (a) The camera falls 50 m with a free-fall acceleration, starting with v i = −10 m s . Its velocity when it reaches the ground is v f = v i2 + 2 a( ∆y ) = ( −10 ( ) m s ) + 2 − 9.80 m s 2 ( −50 m ) = − 33 m s . 2 The time to reach the ground is given by t= v f − vi a = − 33 m s − ( −10 m s ) − 9.80 m s 2 = 2.3 s . (b) This velocity was found to be v f = − 33 m s in part (a) above. 2.51 (a) The keys have acceleration a = − g = -9.80 m s 2 from the release point until they are 1 caught 1.50 s later. Thus, ∆y = v i t + at 2 gives 2 ( ) 2 ∆y − at 2 2 ( + 4.00 m ) − − 9.80 m s (1.50 s ) 2 = = + 10.0 m s , vi = 1.50 s t 2 or v i = 10.0 m s u p w a r d . (b) The velocity of the keys just before the catch was ( ) v f = v i + at = 10.0 m s + − 9.80 m s 2 (1.50 s ) = − 4.68 m s , or 4.68 m s d o w n w a r d . 39 CHAPTER 2.52 2 ( ) 1 1 In this case, ∆y = v i t + at 2 yields −30.0 m = ( −8.00 m s ) t + −9.80 m s 2 t 2 , 2 2 or ( ) 4.90 t 2 + ( 8.00 s ) t + ...
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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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