Daniel walks directly toward a plane mirror at a speed of `0.25 (m)/(s)`. Determine the speed of the image relative to him.

Options

A. `0.13 m/s`
B. `0.50 m/s`
C. `0.25 m/s`
D. `0.75 m/s`

Answer

To solve the problem of determining the speed of Daniel's image relative to him as he walks toward a plane mirror at a speed of 0.25 m/s, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the velocities involved**:
- Let the speed of Daniel (the object) be \( v_D = 0.25 \, \text{m/s} \) toward the mirror.
- The image formed by the plane mirror will move at the same speed as Daniel but in the opposite direction.

2. **Determine the speed of the image**:
- The speed of the image \( v_I \) relative to the ground is equal to the speed of Daniel, but since the image appears to move away from the mirror, we consider it as moving in the opposite direction. Thus, \( v_I = 0.25 \, \text{m/s} \) away from the mirror.

3. **Calculate the relative speed of the image with respect to Daniel**:
- The relative speed of the image with respect to Daniel is given by:
\[ v_{rel} = v_I + v_D \]
- Here, both speeds are in the same direction when considering the relative motion. Therefore:
\[ v_{rel} = 0.25 \, \text{m/s} + 0.25 \, \text{m/s} = 0.50 \, \text{m/s} \]

4. **Conclusion**:
- The speed of the image relative to Daniel is \( 0.50 \, \text{m/s} \).

### Final Answer:
The speed of the image relative to Daniel is \( 0.50 \, \text{m/s} \).

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