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 will use the principle of conservation of momentum. Here are the steps to find the speed of the trolley after the monkey jumps off:

### Step-by-Step Solution:

1. **Identify the masses and initial speed:**
- Mass of the monkey, \( m = 20 \, \text{kg} \)
- Mass of the trolley, \( M = 40 \, \text{kg} \)
- Initial speed of both the monkey and the trolley, \( U = 8 \, \text{m/s} \)

2. **Calculate the initial momentum:**
- The initial momentum of the system (monkey + trolley) can be calculated as:
\[ \text{Initial Momentum} = (m + M) \cdot U = (20 \, \text{kg} + 40 \, \text{kg}) \cdot 8 \, \text{m/s} = 60 \, \text{kg} \cdot 8 \, \text{m/s} = 480 \, \text{kg m/s} \]

3. **Set up the final momentum equation:**
- After the monkey jumps off, it moves vertically and does not contribute to the horizontal momentum. The final momentum of the system is the momentum of the trolley alone:
\[ \text{Final Momentum} = M \cdot V \]
- Here, \( V \) is the final speed of the trolley after the monkey has jumped off.

4. **Apply conservation of momentum:**
- According to the conservation of momentum, the initial momentum equals the final momentum:
\[ \text{Initial Momentum} = \text{Final Momentum} \]
\[ 480 \, \text{kg m/s} = 40 \, \text{kg} \cdot V \]

5. **Solve for \( V \):**
- Rearranging the equation gives:
\[ V = \frac{480 \, \text{kg m/s}}{40 \, \text{kg}} = 12 \, \text{m/s} \]

6. **Conclusion:**
- The speed of the trolley after the monkey has jumped off is \( V = 12 \, \text{m/s} \).