Two billiard balls move toward each other on a table. The mass of the number three ball, m1, is 5 g with a velocity of 3 m/s. The mass of the eight ball, m2, is 6 g with a velocity of 1 m/s. After the balls collide, they bounce off each other. The number three ball moves off with a velocity of 5 m/s. What is the final velocity and direction of the eight ball?

Take the number three ball’s original direction as positive. The initial momentum is (5 g)(3 m/s) + (6 g)(−1 m/s) = 9 g·m/s. Since the balls bounce off each other, the number three ball reverses direction, so its final velocity is −5 m/s. Momentum conservation gives 9 = (5)(−5) + 6v, so v = +5.7 m/s. The eight ball’s final velocity is +5.7 m/s, in the number three ball’s original direction.

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