A boy of mass 50 kg jumps with horizontal velocity of 1 m/s on to a stationary cart. If mass of the cart will be [Assume friction between the wheels the cart and road is zero ]

Options

A. ` 10/11` m/s
B. ` 11/10` m/s
C. `0*65 ` m/s
D. `0*8` m/s

Answer

To solve the problem, we will use the principle of conservation of linear momentum.

### Step-by-Step Solution:

1. **Identify the masses and velocities:**
- Mass of the boy, \( m_b = 50 \, \text{kg} \)
- Initial horizontal velocity of the boy, \( v_b = 1 \, \text{m/s} \)
- Mass of the cart, \( m_c = 5 \, \text{kg} \)
- Initial velocity of the cart, \( v_c = 0 \, \text{m/s} \) (since it is stationary)

2. **Calculate the initial momentum of the system:**
- The initial momentum \( P_i \) of the system (boy + cart) can be calculated as:
\[ P_i = m_b \cdot v_b + m_c \cdot v_c \]
- Substituting the values:
\[ P_i = (50 \, \text{kg} \cdot 1 \, \text{m/s}) + (5 \, \text{kg} \cdot 0 \, \text{m/s}) = 50 \, \text{kg m/s} \]

3. **Set up the final momentum equation:**
- After the boy jumps onto the cart, the total mass of the system is \( m_b + m_c = 50 \, \text{kg} + 5 \, \text{kg} = 55 \, \text{kg} \).
- Let \( V \) be the final velocity of the boy and the cart together. The final momentum \( P_f \) is given by:
\[ P_f = (m_b + m_c) \cdot V = 55 \, \text{kg} \cdot V \]

4. **Apply the conservation of momentum:**
- According to the conservation of momentum, the initial momentum equals the final momentum:
\[ P_i = P_f \]
- Substituting the values we calculated:
\[ 50 \, \text{kg m/s} = 55 \, \text{kg} \cdot V \]

5. **Solve for the final velocity \( V \):**
- Rearranging the equation to solve for \( V \):
\[ V = \frac{50 \, \text{kg m/s}}{55 \, \text{kg}} = \frac{10}{11} \, \text{m/s} \]

6. **Conclusion:**
- The final velocity of both the boy and the cart after the boy jumps onto the cart is \( V = \frac{10}{11} \, \text{m/s} \).