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## Homework Statement

Prove that in an elastic collision between two identical bodies, one of which is initially at rest, the angle between their velocities after collision is pi/2, except for the case of central impact.

## Homework Equations

Assume particle 1 travels in the x direction with speed v1(before) and strikes particle 2, which is at rest. After the collision, particle 1 makes an angle theta1 with the x axis, and particle 2 makes angle theta2. We need to show that theta1 + theta2 = pi/2.

*Conservation of linear momentum*

mv1(before) = SUM(mvi(after))

x component: mv1(before) = mv1(after) cos(theta1) + mv2(after) cos(theta2)

y component: 0 = mv2(after) sin(theta2) - mv1(after) sin(theta1)

*Conservation of kinetic energy*

.5mv1(before)^2 = .5mv1(after)^2 + .5mv2(after)^2

## The Attempt at a Solution

I'm afraid I really don't know what to do with this. I notice that if theta1 + theta2 form a right angle, then by the Pythagorean theorem,

v1(after)^2 + v2(after)^2 = [v1(after) sin(theta1) + v2(after) sin(theta2)]^2

= v1(after)^2 sin^2(theta1) + (2)(v1(after))(v2(after)) sin(theta1) sin(theta2) + v2(after)^2 sin^2(theta2)

But this doesn't really look very useful. Hint please?