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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 = ( âˆ†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 = ( âˆ†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 = âˆ’ g = âˆ’9.80 m s 2 , is found from âˆ†y = v i t + at 2 as
2 t down = 2 ( âˆ†y ) a = 2 ( âˆ’ 308 m )
âˆ’ 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 freefall acceleration, starting with v i = âˆ’10 m s . Its
velocity when it reaches the ground is
v f = v i2 + 2 a( âˆ†y ) = ( âˆ’10 ( ) m s ) + 2 âˆ’ 9.80 m s 2 ( âˆ’50 m ) = âˆ’ 33 m s .
2 The time to reach the ground is given by t= v f âˆ’ vi
a = âˆ’ 33 m s âˆ’ ( âˆ’10 m s )
âˆ’ 9.80 m s 2 = 2.3 s . (b) This velocity was found to be v f = âˆ’ 33 m s in part (a) above. 2.51 (a) The keys have acceleration a = âˆ’ g = 9.80 m s 2 from the release point until they are 1
caught 1.50 s later. Thus, âˆ†y = v i t + at 2 gives
2 ( ) 2
âˆ†y âˆ’ at 2 2 ( + 4.00 m ) âˆ’ âˆ’ 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 + âˆ’ 9.80 m s 2 (1.50 s ) = âˆ’ 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, âˆ†y = v i t + at 2 yields âˆ’30.0 m = ( âˆ’8.00 m s ) t + âˆ’9.80 m s 2 t 2 ,
2
2
or ( ) 4.90 t 2 + ( 8.00 s ) t + âˆ...
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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.
 Spring '05
 Dr.Ha
 Physics, Acceleration

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