A ball is thrown from the ground with velocity `u` at an angle `theta` with horizontal. If the coefficient of restitution is `e` , find the time of flight , the maximum height and the horizontal range after the first collision.

Explanation

To solve the problem of a ball thrown from the ground with an initial velocity \( u \) at an angle \( \theta \) with the horizontal, and considering the coefficient of restitution \( e \), we will find the time of flight, maximum height, and horizontal range after the first collision with the ground.

### Step-by-Step Solution:

1. **Understanding the Components of Motion:**
- The initial velocity \( u \) can be broken down into horizontal and vertical components:
- Horizontal component: \( u_x = u \cos \theta \)
- Vertical component: \( u_y = u \sin \theta \)
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