The relative velocity of two objects A and B is 10 m/s. If the velocity of object A is 40 m/s then the velocity with which B is moving is (assume both objects are moving in same direction)

Options

A. 10 m/s
B. 40 m/s
C. 30 m/s
D. 15 m/s

Answer

To find the velocity of object B given the relative velocity of objects A and B, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Relative Velocity**:
The relative velocity of two objects moving in the same direction is given by the formula:
\[ V_{AB} = V_A - V_B \]
where \( V_{AB} \) is the relative velocity of A with respect to B, \( V_A \) is the velocity of A, and \( V_B \) is the velocity of B.

2. **Identify the Given Values**:
- Relative velocity \( V_{AB} = 10 \, \text{m/s} \)
- Velocity of object A \( V_A = 40 \, \text{m/s} \)

3. **Set Up the Equation**:
Using the formula for relative velocity:
\[ 10 = 40 - V_B \]

4. **Rearrange the Equation to Solve for \( V_B \)**:
To find \( V_B \), rearrange the equation:
\[ V_B = 40 - 10 \]

5. **Calculate the Velocity of Object B**:
\[ V_B = 30 \, \text{m/s} \]

### Final Answer:
The velocity with which object B is moving is \( 30 \, \text{m/s} \).

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