A monkey of mass 20 kg rides on a 40 kg trolley moving at a constant speed of 8 m/s along a horizontal track. Frictional force can be neglected. If the monkey jumps vertically, with respect to the moving trolley, the catch the overhanging branch of tree, the speed of the trolley after the monkey has jumped off is :-

Options

A. 16 m/s
B. 12 m/s
C. 8 m/s
D. 6 m/s

Answer

To solve the problem, we need to analyze the situation when the monkey jumps off the trolley.

### Step-by-Step Solution:

1. **Identify the Initial Conditions**:
- Mass of the monkey (m₁) = 20 kg
- Mass of the trolley (m₂) = 40 kg
- Initial speed of both the monkey and the trolley (v₀) = 8 m/s

2. **Understand the Motion**:
- The monkey jumps vertically upward with respect to the trolley. This means that while the monkey gains vertical velocity, it retains the horizontal velocity of the trolley at the moment of the jump.

3. **Apply the Principle of Conservation of Momentum**:
- Since there are no external horizontal forces acting on the system (the frictional force is neglected), the horizontal momentum of the system must be conserved.
- Initial momentum of the system (before the jump) = (mass of monkey + mass of trolley) × initial velocity
- Initial momentum = (m₁ + m₂) × v₀ = (20 kg + 40 kg) × 8 m/s = 480 kg·m/s

4. **Analyze the Situation After the Jump**:
- When the monkey jumps off, it retains the horizontal speed of the trolley at the moment of the jump, which is 8 m/s.
- The trolley continues to move forward without any change in its horizontal speed because there is no external force acting on it.

5. **Final Speed of the Trolley**:
- After the monkey jumps off, the speed of the trolley remains the same as it was before the jump, which is 8 m/s.

### Conclusion:
The speed of the trolley after the monkey has jumped off is **8 m/s**.