A ball of radius `R=20 cm` has mass `m=0.75 kg` and moment of inertia (about its diameter ) `I=0.0125 kgm^(2)`. The ball rolls without sliding over a rough horizontal floor wilth velocity `v_(0)=10 ms^(-1)` towards a smooth vertical wall if coefficient of resutitution between the wall and the ball is `e=0.7`, calculate velocity `v` of the ball long after the collision. `(g=10ms^(-2))`

Explanation

To solve the problem step by step, we will use the concept of the coefficient of restitution and the properties of rolling motion.

### Step 1: Understanding the initial conditions
The ball has the following properties:
- Radius \( R = 20 \, \text{cm} = 0.2 \, \text{m} \)
- Mass \( m = 0.75 \, \text{kg} \)
- Moment of inertia about its diameter \( I = 0.0125 \, \text{kg m}^2 \)
- Initial velocity \( v_0 = 10 \, \text{m/s} \)
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