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2015-03-02T20:47:13+05:30

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Let us say the ball loses half of its energy after impact on the ground.  The loss happens due to inelastic collision.

Initial Potential Energy of the ball = m g h
Total energy in the ball = KE + PE = m g h

Suppose it loses  1/n th part of its energy. then  1 - 1/n is the remaining energy.
         Total energy after impact = m g h (n-1)/n
   It will rise to  a height of  h*(n-1)/n

suppose n = 2,  that is the ball loses half of its energy on impact.  Then,
         the height will be = h/2

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