Question

A ball dropped from a height of 10m loses of its energy after impact on ground. how much height will it gain after one impact

Answer 1

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