A boy of mass `m` is riding on a trolley of mass `M` which is moving on smooth floor at speed `v_(0)`. He jumps off in the opposite direction of motion of trolley with velocity `u` relative to the trolley before the jump. Find the velocity of the trolley after jump.

Explanation

To solve the problem, we will use the principle of conservation of momentum. Here are the steps to find the velocity of the trolley after the boy jumps off:

### Step 1: Understand the Initial Conditions
Initially, both the boy and the trolley are moving together with a velocity \( v_0 \). The total mass of the system is \( M + m \), where \( M \) is the mass of the trolley and \( m \) is the mass of the boy.

### Step 2: Define the Final Conditions
After the boy jumps off the trolley, he jumps in the opposite direction of the trolley's motion with a velocity \( u \) relative to the trolley. We need to find the final velocity \( V \) of the trolley after the boy jumps.

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