When two billiard balls collide the collision is assumed to be elastic. Show that for a general case, where the collision is not head on, the cue ball moves in a direction perpendicular to the direction of the object ball, after impact. Assume that the balls have the same mass and the object ball is initially at rest.

$m\vec{V}_{1A}=m\vec{V}_{2A}+m\vec{V}_{2B}\\ =>\vec{V}_{1A}=\vec{V}_{2A}+\vec{V}_{2B}\\\\ mV_{1A}^2/2=mV_{2B}^2/2+mV_{2A}^2/2\\ =>V_{1A}^2/2=V_{2B}^2/2+V_{2A}^2/2\\ =>V_{1A}^2=V_{2B}^2+V_{2A}^2\\ by\,pythagoras\,theorem,\,\vec{V}_{2A},\vec{V}_{2B}\,are\,perpendicular$
`Lelts assume A only a is moving before collisionsince the collison is elastic so KE is conserved$m\vec{V}_{1A}=m\vec{V}_{2A}+m\vec{V}_{2B}\\ =>\vec{V}_{1A}=\vec{V}_{2A}+\vec{V}_{2B}\\\\ mV_{1A}^2/2=mV_{2B}^2/2+mV_{2A}^2/2\\ =>V_{1A}^2/2=V_{2B}^2/2+V_{2A}^2/2\\ =>V_{1A}^2=V_{2B}^2+V_{2A}^2\\ by\,pythagoras\,theorem,\,\vec{V}_{2A},\vec{V}_{2B}\,are\,perpendicular$Arun KumarIIT DelhiAskiitians Faculty`