A child is standing at one end of a long trolley moving with a speed v on a smooth horizontal track. If the child starts running towards the other end of the trolley with a speed u, the centre of mass of the system (trolley + child) will move with a speed :

Explanation

To solve the problem of the child running on the trolley, we can follow these steps:

### Step 1: Understand the Initial Conditions
- The trolley is moving with a speed \( V \) on a smooth horizontal track.
- The child is initially standing at one end of the trolley, so the child's initial speed with respect to the ground is also \( V \).

### Step 2: Define the Masses
- Let the mass of the child be \( m_1 \).
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