Question

A billiard ball at rest is struck by another ball of the same mass whose speed is 5 m/s. After an elastic collision the incident goes off at an angle of 40 degrees with respect to its original direction of motion and the struck ball goes off at an at an angle of 50 degrees with respect to this original direction. Find the final speed of both balls.

Answer 1

Px = x momentum = 5 m
Py = y momentum = 0
Ke = (1/2) m * 25 = 12.5 m
all of those are the same later
Px = m u1 + mu2 = 5 m so u1 + u2 = 5
u1 = Speed1 cos 40
u2= Speed2 cos 50
and
v1 = Speed1 sin 40
v2 = Speed2 sin 50
so Speed1 sin 40 + Speed2 sin 50 = 0
and
KE/m = u1^2 + u2^2 + v1^2 + v2^2 = 12.5