Question

A drawing of two billiard balls before, during, and after a collision. An arrow pointing left shows negative direction and an arrow pointing right shows the positive direction. In the before diagram, there is a billiard ball on the left labeled m Subscript 1 Baseline with a velocity vector to the right labeled v Subscript 1 Baseline 3 meters per second. The second ball is on the right labeled m Subscript 2 Baseline with a velocity vector to the left labeled v Subscript 2 Baseline = negative 1 meters per second. In the during diagram, the two balls are touching with equal vectors away from each other. In the After diagram, the billiard ball on the left is labeled m Subscript 1 Baseline with a velocity vector to the left labeled v Subscript 1 f Baseline = negative 5 meters per second. The ball on the right is labeled m Subscript 2 Baseline, labeled v Subscript 2 f Baseline = unknown.
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?

+8.6 m/s
+5.7 m/s
–5.7 m/s
–8.6 m/s

Answer 1

Use conservation of momentum (no external impulse):

m1 v1i + m2 v2i = m1 v1f + m2 v2f.

Using grams (they cancel units):
5·3 + 6·(−1) = 5·(−5) + 6·v2f
15 − 6 = −25 + 6 v2f
9 = −25 + 6 v2f
6 v2f = 34 → v2f = 34/6 ≈ 5.67 m/s.

So the eight ball moves at about +5.7 m/s (to the right). Answer: +5.7 m/s.