A plane mirror and an object has speeds of `5 m//s "and" 10 m//s` respectively. If the motion of mirror and object is along the normlal of the mirror then the speed of image may be:-

Options

A. 0m/s
B. 10m/s
C. 20m/s
D. 25m/s

Explanation

To solve the problem of finding the speed of the image formed by a plane mirror when both the mirror and the object are in motion, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Speed of the mirror, \( v_m = 5 \, \text{m/s} \)
- Speed of the object, \( v_o = 10 \, \text{m/s} \)

2. **Understand the Motion**:
- The motion of both the mirror and the object is along the normal to the mirror.
- Since they are moving in opposite directions, we will consider the speeds as positive in our calculations.

3. **Use the Formula for Speed of Image**:
- The speed of the image \( v_i \) formed by a plane mirror when the object and the mirror are moving is given by:
\[ v_i = 2v_m + 2v_o \]
- Here, \( v_i \) is the speed of the image, \( v_m \) is the speed of the mirror, and \( v_o \) is the speed of the object.

4. **Substitute the Values**:
- Plugging in the values we have:
\[ v_i = 2(5) + 2(10) \]

5. **Calculate**:
- Calculate each term:
\[ v_i = 10 + 20 = 30 \, \text{m/s} \]

6. **Conclusion**:
- The speed of the image is \( 30 \, \text{m/s} \).

### Final Answer:
The speed of the image is \( 30 \, \text{m/s} \).

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