A massive ball (A) is dropped from height h on a smooth horizontal floor. A smaller ball (B) is also dropped simultaneously. Initially ball B was just touching ball A (see fig.). Radii of both balls is much smaller than h. Ball A hits the floor, rebounds and immediately hits B. Motion of both the balls is vertical before the collision of two balls. All collision are elastic and there is no friction. Ball B lands at point P on the ground after colliding with A. Find OP, assuming that it is large compared to radius of A.

Answer

`16hsin 2 theta[(1)/(2)+cos 2 theta]`