Two trolleys `A` and `B` are free to move on a level frictionless track, and are initially stationary. A man on trolley `A` throws a bag of mass `10 kg` with a horizontal velocity of `4 ms^(-1)` with respect to himself on to trolley `B` of mass `100 kg`. The combined mass of trolley `A` (excluding bag) and the man is `140 km`. Find the ratio of velocities of trolleys `A` and `B`, just after the bag lands on trolley `B`.

Explanation

To solve the problem, we will apply the principle of conservation of momentum. The steps are as follows:

### Step 1: Understand the initial conditions
- Trolley A has a mass \( m_A = 140 \, \text{kg} \) (combined mass of trolley A and the man).
- Trolley B has a mass \( m_B = 100 \, \text{kg} \).
- The bag has a mass \( m_{bag} = 10 \, \text{kg} \).
- The initial velocity of both trolleys is \( 0 \, \text{m/s} \).

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