A projectile aimed at a mark in the horizontal plane through the point of projection…

PHYSICS · Subjective · CBSE · Physics · Motion in a Plane · Motion in a Plane

Problem

A projectile aimed at a mark 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}

beyond it when the elevation is

\beta

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

\frac{1}{2}\sin^{-1}\left(\frac{b\sin 2\alpha+a\sin 2\beta}{a+b}\right).