A body is allowed to fall freely under gravity from a height of 10 m. If it loses 25% of its energy on impact with the ground, to what height will it rise after one impact?

A body is allowed to fall freely under gravity from a height of 10 m.

1.	A body is allowed to fall freely under gravity from a height of 10 m. If it loses 25% of its energy on impact with the ground, to what height will it rise after one impact?
Answer» 2.5 m 5.0 m 7.5 m 9.0 m Solution :Height `h= 10 m`. POTENTIAL energy at this height = mgh. On reaching the ground, KE = mgh. SINCE the body loses 25% of energy due to IMPACT, KINETIC energy of the body after one impact = 0.75 mgh. If `v_1` is the initial upward velocity after the impact , we have `1/2 mv_1^2 = 0.75 mgh = 3/4 mgh" or " v_1^2 = 1.5 gh` The height `h_1` to which the bocy will rise is `h_1 = (v_1^2)/(2g) = (1.5gh )/(2g) = 0.75 h = 0.75 xx 10 = 7.5 m ( :. h = 10M). `