The rule is generically valid for *elastic* collisions between *equal mass* objects when *one is stationary* before the collision. A short proof is to square the magnitude of each side of the vector version of the equation of momentum conservation:\\ \\
{latex}\begin{large} \[ m^{2}v_{1,i}^{2} = m^{2}(v_{1,f}^{2} + 2\vec{v}_{1,f}\cdot \vec{v}_{2,f} + v_{2,f}^{2}) \]\end{large}{latex} \\
Cancelling the masses and comparing to the equation of kinetic energy conservation will immediately yield the result that \\
{latex}\begin{large}\[ \vec{v}_{1,f}\cdot\vec{v}_{2,f} = 0 \]\end{large}{latex}
which implies that (a.) one of the objects has zero final velocity or else (b.) the objects move at right angles to one another after the collision. |