A body is projected up with a velocity equal to 3 / 4 th of the escape velocity from the surface of the earth. The height it reaches is, (Radius of earth = R )

Step-by-step solution

Escape velocity for the earth is v e = 2 G M R Given the velocity projection of the body = v = 3 4 v e = 3 4 2 G M R Total energy on the earth = T o t a l e n e rg y a t m a x i m u m h e i g h t h 1 2 m v 2 + - G M m R = 0 + - G M m R + h 1 2 m . 9 16 . 2 G M R - G M m R = - G M m R + h 9 16 - 1 = - R R + h or - R R + h = - 7 16 7 R + 7 h = 16 R 7 h = 9 R ⇒ h = 9 7 R