A body is fired with velocity of magnitude $\sqrt{gR} < V< \sqrt{2gR}$ at an angle of 30° with the radius vector of earth. If at the highest point the speed of the body is v/4, the maximum height attained by the body is equal to  

where R = radius of earth. (Use the appropriate assumptions)

R

Conservation of angular momentum of the body about O yields

mv (sin 30) R = mv' (R + h)

⇒ $\frac{v}{2} R=\frac{v}{4}(R+h)$

⇒ h = R.