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 solve the problem of finding the velocity of object B given the relative velocity between objects A and B, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Relative Velocity**:
- The relative velocity of object A with respect to object B (denoted as \( V_{AB} \)) is defined as the velocity of A minus the velocity of B when both objects are moving in the same direction.
- Mathematically, this can be expressed as:
\[ V_{AB} = V_A - V_B \]

2. **Identify Given Values**:
- From the problem, we know:
- The relative velocity \( V_{AB} = 10 \, \text{m/s} \)
- The velocity of object A \( V_A = 40 \, \text{m/s} \)

3. **Set Up the Equation**:
- Plugging the known values into the relative velocity equation:
\[ 10 = 40 - V_B \]

4. **Solve for \( V_B \)**:
- Rearranging the equation to isolate \( V_B \):
\[ V_B = 40 - 10 \]
- Calculating the right side:
\[ V_B = 30 \, \text{m/s} \]

5. **Conclusion**:
- The velocity of object B is \( 30 \, \text{m/s} \).

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

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