Problem

A projectile aimed at a mark, which is in the horizontal plane through the point of projection, falls

a \text{ cm}

short of it when the elevation is

\alpha

and goes

b \text{ cm}

far when the elevation is

\beta

. Show that, if the speed of projection is same in all the cases the proper elevation is

\frac{1}{2} \sin^{-1} \left[ \frac{b \sin 2\alpha + a \sin 2\beta}{a + b} \right]