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395_Physics ProblemsTechnical Physics

395_Physics ProblemsTechnical Physics - Chapter 13*P13.43(a...

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Chapter 13 397 *P13.43 (a) Energy conservation for the object-Earth system from firing to apex: K U K U mv GmM R GmM R h g i g f i E E E E + = + = + e j e j 1 2 0 2 where 1 2 mv GmM R E E esc 2 = . Then 1 2 1 2 1 2 1 2 2 2 2 2 2 2 2 v v v R R h v v v R R h v v R h v R h v R v v R v R v R v R v v h R v v v i E E i E E i E E E i E E E i E i E i i = − + = + = + = = + = esc 2 esc 2 esc 2 esc 2 esc 2 esc 2 esc 2 esc 2 esc 2 esc 2 esc 2 esc 2 (b) h = × = × 6 37 10 11 2 8 76 1 00 10 6 2 2 2 7 . . . . m 8.76 m a f a f a f (c) The fall of the meteorite is the time-reversal of the upward flight of the projectile, so it is described by the same energy equation v v R R h v h R h v i E E E i 2 2 2 3 2 7 6 7 8 4 1 11 2 10 2 51 10 6 37 10 2 51 10 1 00 10 1 00 10 = + F H G I K J = + F H G I K J = × × × + × F H G I K J = × = × esc esc 2 2 m s m m m m s m s . . . . . . e j (d) With v v i << esc , h R v v R v R GM E i E i E E = 2 2 2 2 esc . But g GM R E E = 2 , so h v g i = 2 2 , in agreement with
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