A boy walks at a speed of 5 m/s towards a plane mirror. The boy and his image in the mirror are moving:

Options

A. towards each other at a speed of 5 m/s
B. away from each other at a speed of 5 m/s
C. towards each other at a speed of 10 m/s
D. away from each other at a speed of 10 m/s

Explanation

To solve the problem, we need to analyze the situation of a boy walking towards a plane mirror and how his image behaves in relation to him.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- The boy is walking towards a plane mirror at a speed of 5 m/s.
- A plane mirror creates an image of the boy that appears to be the same distance behind the mirror as the boy is in front of it.

2. **Distance to the Mirror**:
- Let's assume the boy is at a distance 'd' from the mirror. As he walks towards the mirror, this distance decreases.

3. **Speed of the Boy**:
- The speed of the boy is given as 5 m/s towards the mirror.

4. **Speed of the Image**:
- The image in the mirror will appear to move towards the boy at the same speed as the boy is moving towards the mirror. Thus, the image also appears to move towards the boy at 5 m/s.

5. **Relative Speed**:
- Since both the boy and his image are moving towards each other, we need to add their speeds to find the relative speed between them.
- Speed of the boy = 5 m/s (towards the mirror)
- Speed of the image = 5 m/s (towards the boy)
- Therefore, the relative speed = Speed of the boy + Speed of the image = 5 m/s + 5 m/s = 10 m/s.

6. **Conclusion**:
- The boy and his image in the mirror are moving towards each other at a speed of 10 m/s.

### Final Answer:
The boy and his image in the mirror are moving towards each other at a speed of 10 m/s.

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