A man runs towards a mirror at a rate of 6m`s^(-1)` . If the mirror is at rest, his image will have a velocity (with respect to man)

Options

A. `+12 ms^(-1)`
B. `-6ms^(-1)`
C. `6ms^(-1)`
D. `-12ms^(-1)`

Explanation

To solve the problem, we need to determine the velocity of the image of the man as he runs towards a stationary mirror.

### Step-by-Step Solution:

1. **Understanding the Situation**:
- The man is running towards a plane mirror at a speed of 6 m/s.
- The mirror is stationary.

2. **Velocity of the Man**:
- The velocity of the man (V_m) is given as +6 m/s (towards the mirror).

3. **Velocity of the Image**:
- In a plane mirror, the image moves at the same speed as the object but in the opposite direction.
- Therefore, the velocity of the image (V_i) will be -6 m/s (since it is moving away from the mirror).

4. **Relative Velocity of the Image with respect to the Man**:
- To find the velocity of the image with respect to the man, we use the formula:
\[ V_{im} = V_i - V_m \]
- Substituting the values:
\[ V_{im} = (-6 \, \text{m/s}) - (6 \, \text{m/s}) = -12 \, \text{m/s} \]

5. **Conclusion**:
- The negative sign indicates that the image is moving in the opposite direction to the man. Thus, the velocity of the image with respect to the man is 12 m/s towards the mirror.

### Final Answer:
The velocity of the image with respect to the man is -12 m/s (or 12 m/s towards the mirror).

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