2 s 980 m s 2 a b the final velocity is v f 0 980

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Unformatted text preview: d v f 2.62 ( ) = v iK + aK t = 0 + 4.90 m s 2 ( 5.46 s ) = 26.7 m s , ( ) = v iS + aS ( t + 1.00 s ) = 0 + 3.50 m s 2 ( 6.46 s ) = 22 .6 m s . (a) The velocity with which the first stone hits the water is 2 m⎞ m⎞ m ⎛ ⎛ 2 v 1 f = − v 1i + 2 a( ∆y ) = − ⎜ − 2 .00 ⎟ + 2 ⎜ − 9.80 2 ⎟ ( −50.0 m ) = −31.4 . ⎝ ⎝ s⎠ s⎠ s The time for this stone to hit the water is t1 = v 1 f − v 1i a ⎡ −31.4 m s − ( −2 .00 m s ) ⎦ ⎤ =⎣ = 3.00 s . 2 -9.80 m s (b) Since they hit simultaneously, the second stone which is released 1.00 s later, will hit the water after an flight time of 2.00 s. Thus, ( ) 2 2 ∆y − at 2 2 −50.0 m − −9.80 m s ( 2 .00 s ) 2 v 2i = = = − 15.2 m s . t2 2.00 s 2 (c) From part (a), the final velocity of the first stone is v 1 f = − 31.4 m s . The final velocity of the second stone is ( ) v 2 f = v 2i + at 2 = −15.2 m s + −9.80 m s 2 ( 2.00 s ) = − 34.8 m s . 2.63 (a) At 5.00 m above the surface, the velocity of the astronaut is given by ( ) v f = v i2 + 2 a( ∆y ) = 0 + 2 2 .00 m s 2 ( 5.00 m ) = + 4.47 m s . (b) The bolt begins free-fall with an initial velocity of v f = + 4.47 m s at 5.00 m above 1 the surface. When it reaches the surface, ∆y = v i t + at 2 gives 2 1 −5.00 m = ( +4.47 m s ) t + −1.67 m s 2 t 2 which has a positive solution of t = 6.31 s . 2 Thus, the bolt hits 6.31 s after it is released . ( ) 45 CHAPTER 2 (c) When it reaches the surface, the velocity of the bolt is ( ) v f = v i + at = + 4.47 m s + −1.67 m s 2 ( 6.31 s ) = − 6.06 m s . (d) The displacement of the astronaut while the bolt is falling is ( ) 1 1 2 ∆y = v i t + at 2 = ( 4.47 m s ) ( 6.31 s ) + 2 .00 m s 2 ( 6.31 s ) = 68.0 m . 2 2 Therefore, the altitude of the astronaut when the bolt hits is y f = 5.00 m + 68.0 m = 73.0 m . (e) The velocity of the astronaut when the bolt hits is ( ) v f = v i + at = + 4.47 m s + + 2 .00 m s 2 ( 6.31 s ) = + 17.1 m s . 2.64 1 (a) From ∆y = v i t + at 2 with v i = 0 , we have...
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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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