A man runs towards a mirror at a speed 15 m/s. The speed of the image relative to the man is

Options

A. (a)15ms^(-1)`
B. (b)`30ms^(-1)`
C. (c)`35ms^(-1)`
D. (d)`20ms^(-1)`

Answer

To solve the problem of finding the speed of the image relative to the man running towards a mirror at a speed of 15 m/s, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Speeds**:
- The speed of the man (Vm) towards the mirror is 15 m/s.
- The speed of the image (Vi) in the mirror is also 15 m/s, but it moves towards the man.

2. **Set Up the Relative Speed Equation**:
- The speed of the image relative to the man (V_rel) can be calculated using the formula:
\[ V_{rel} = V_i - V_m \]
- Here, \(V_i\) is the speed of the image, and \(V_m\) is the speed of the man.

3. **Substitute the Values**:
- Since both the man and the image are moving towards each other, we consider the direction of the speeds:
\[ V_{rel} = 15 \, \text{m/s} - (-15 \, \text{m/s}) \]
- The negative sign indicates that the man is moving towards the mirror, while the image is also moving towards him.

4. **Calculate the Relative Speed**:
- Simplifying the equation:
\[ V_{rel} = 15 + 15 = 30 \, \text{m/s} \]

5. **Conclusion**:
- The speed of the image relative to the man is 30 m/s.

### Final Answer:
The speed of the image relative to the man is **30 m/s**.

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