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Question

A particle is projected upward from the surface of earth(radius R) with a K.E. equal to half the minimum value needed for it to escape from earth's gravity. To what height does it rises above the surface of earth?

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Solution

KE needed to escape from the surface:
E=12mve2 =12m2Gmr2 =12m2Gmr =GMmr

PE at the surface of Earth + 12E= PE at the maximum height
-GMmr+12GMmr=-GMmr+h-12GMmr=-GMmr+h 12r=1r+h 2r=r+h h=r

Answer: h = r

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