A ball of mass m moving at a speed v makes a head-on collision with an identical ball at rest. The kinetic energy of the balls after the collision is three fourths of the original. Find the coefficient of restitution.

Explanation

To solve the problem step by step, we will analyze the situation of the collision between two identical balls, one of which is initially at rest. We will use the principles of conservation of momentum and kinetic energy to find the coefficient of restitution.

### Step 1: Understand the Initial Conditions
- We have two identical balls, each with mass \( m \).
- One ball is moving with speed \( v \), and the other ball is at rest.
- The initial kinetic energy of the moving ball is given by:
\[
KE_{\text{initial}} = \frac{1}{2} m v^2
...