A smooth wedge of mass M is kept at rest on a smooth horizontal surface . Inclined face of the wedge make an angle `theta ` with the horizontal . A particle of mass m collides normal to inclined face of wedge . If speed of the particle just before collision is u and coefficient of restitution is `e` then find velocity of wedge after collision .

Explanation

To solve the problem of finding the velocity of the wedge after the collision, we will follow these steps:

### Step 1: Understand the system
We have a wedge of mass \( M \) on a smooth horizontal surface, and a particle of mass \( m \) colliding with the wedge's inclined face at an angle \( \theta \). The initial speed of the particle before the collision is \( u \).

### Step 2: Apply conservation of momentum
Since there are no external forces acting on the system in the horizontal direction, we can apply the conservation of momentum. Before the collision, only the particle is moving. After the collision, both the wedge and the particle will be moving.

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