The coefficient of restitution between a snooker ball and the side cushion is `1/3`. If the ball hits the cushion and then rebounds at right angles to its original direction, show that the angles made with the side cushion by the direction of motion before and after impact are `60^@` and `30^@` respectively.

Explanation

To solve the problem, we need to analyze the motion of a snooker ball before and after it hits the cushion. The coefficient of restitution (e) is given as \( \frac{1}{3} \). We will denote the angle made with the cushion before impact as \( \alpha \) and after impact as \( \beta \).

### Step-by-Step Solution:

1. **Understanding the Problem:**
- The ball hits the cushion and rebounds at right angles to its original direction.
- The coefficient of restitution \( e \) is defined as the ratio of the relative velocity of separation to the relative velocity of approach.

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