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On a frictionless horizontal table, a ball moving at 10 m/s strikes two identical stationary balls that are touching each other, their line of centres being perpendicular to the incoming ball's velocity. The moving ball heads straight for the point where the two balls touch. Assuming all collisions are perfectly elastic and all three balls have equal mass, find each ball's velocity after impact.

1. Incoming ball rebounds at 2 m/s; the two struck balls each move at 6 m/s at 30 deg to the original direction
2. Incoming ball stops; the two struck balls each move at 5 m/s along the original direction
3. Incoming ball continues at 5 m/s; the two struck balls each move at 2.5 m/s
4. All three balls move at 10/3 m/s

Correct answer: Incoming ball rebounds at 2 m/s; the two struck balls each move at 6 m/s at 30 deg to the original direction

Solution

The two outgoing balls move symmetrically at 30 deg to the original direction. Applying momentum conservation along the line of motion and the elastic-collision (energy) condition gives the incoming ball a rebound speed of 2 m/s and each struck ball 6 m/s.

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