A projectile aimed at a mark, which is in the horizontal plane through the point of projection, falls a cm short of it when the elevation is `alpha` and goes b cm far when the elevation is `beta`. Show that, if the speed of projection is same in all the cases the proper elevation is
`1/2 sin^(-1) [(bsin2alpha+asin2beta)/(a+b)]` .

Explanation

`(1)/(2) sin^(-1)[(a sin 2 alpha a+ b sin 2 beta)/(a+b)]`