Consider an object `P` on an inclined plane of inclination `beta`.
A shot is fired `O` at an angle `alpha` with horizontal. Find the relation between `alpha` and `beta`, if the shot hits the object horizontally.

Explanation

At point `P`, the velocity of shot becomes horizontal, i.e.
`OA = (R )/(2), PA = H_(max)`
`tan beta = (H_(max))/((R )/(2)) = (2 H_(max))/(R )`
`= (2(u^(2) sin^(2) alpha)/(2g))/((u^(2))/(g)(2 sin alpha cos alpha))`
`tan alpha = 2 tan beta`