On the pole of the Earth a body is imparted velocity `v_0` directed vertically up. Knowing the radius of the Earth and the free-fall acceleration on its surface, find the height to which the body will ascend. The air drag is to be neglected.

Explanation

Let the mass of the body be m and let it go upto a height h.
From conservation of mechanical energy of the system
`-(gammaMm)/(R)+1/2mv_0^2=(-gammaMm)/((R+h))=0`
Using `(gammaM)/(R^2)=g`, in above equation and on solving we get,
`h=(Rv_0^2)/(2gR-v_0^2)`