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

Options

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

Explanation

To find the speed of the image relative to the man running towards the mirror, we can follow these steps:

### Step 1: Understand the motion of the man and the image
- The man is running towards the mirror at a speed of 15 m/s.
- In a plane mirror, the image moves at the same speed as the object but in the opposite direction.

### Step 2: Determine the speed of the image
- Since the man is moving towards the mirror at 15 m/s, the image will also be moving towards the mirror at 15 m/s.

### Step 3: Calculate the speed of the image relative to the man
- To find the speed of the image relative to the man, we need to consider the direction of both the man and the image.
- The image moves towards the mirror at 15 m/s (let's consider this as positive).
- The man also moves towards the mirror at 15 m/s (but we will consider this as negative since he is moving towards the image).

### Step 4: Use the relative speed formula
- The relative speed of the image with respect to the man can be calculated as:
\[ \text{Speed of image relative to man} = \text{Speed of image} + \text{Speed of man} \]
\[ = 15 \, \text{m/s} + 15 \, \text{m/s} = 30 \, \text{m/s} \]

### Conclusion
- The speed of the image relative to the man is **30 m/s** towards the mirror.

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