A cue ball travelling at 7.6 m/s strikes the eight ball. The eight ball moves away from the collision at an angle of 22 deg. on one side of the initial line of travel. The cue ball moves away at 33 deg on the other side of the initial line of travel. What are their final speeds? mass of both is the same
Call the final velocities V8 and Vc
Call the initial velcoity of the 8 ball Vo.
Momentum conservation tells you this:
M*Vc cos 33 + M*V8 cos 22 = M*Vo
M*Vc sin 33 = M*V8 sin 22
M is the mass of each ball, and can be cancelled out
You are left with two equations in two unknowns, Vc and V8, to be solved.
Put in the numbers for the sines and cosines, and cancel out the M.
0.8387 Vc + 0.9272 V8 = 7.6
0.5446 Vc + 0.3746 V8 = 0
Kinetic energy is usually very nearly conserved in billiard ball collisions, but you do not have to assume that to solve the problem