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# 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.

Arun Kumar IIT Delhi
7 years ago
elts assume A only a is moving before collision
since 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 Kumar IIT Delhi
`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`