If an observer is walking away from the plane mirror with `6m//sec` . Then the velocity of the image with respect to observer will be

Options

A. `6m//sec`
B. `-6 m//sec`
C. `12 m//sec`
D. `3m//sec`

Explanation

To solve the problem of finding the velocity of the image with respect to the observer walking away from a plane mirror at a speed of 6 m/s, we can follow these steps:

### Step 1: Understand the scenario
The observer is moving away from a plane mirror at a speed of 6 m/s. The image formed by a plane mirror moves in such a way that it appears to be at the same distance behind the mirror as the observer is in front of it.

### Step 2: Determine the speed of the image
Since the observer is moving away from the mirror at 6 m/s, the image will also appear to move away from the mirror at the same speed. Therefore, the speed of the image with respect to the ground is also 6 m/s.

### Step 3: Calculate the relative speed of the image with respect to the observer
To find the velocity of the image with respect to the observer, we need to consider the distance between the observer and the image. The observer is moving away from the mirror, and the image is moving away from the mirror as well.

- The distance between the observer and the image doubles because the observer is moving away from the mirror and the image is also moving away from the mirror.
- Therefore, the relative speed of the image with respect to the observer is the sum of the speeds of the observer and the image.

### Step 4: Perform the calculation
The speed of the observer = 6 m/s
The speed of the image = 6 m/s

Relative speed of the image with respect to the observer = Speed of the observer + Speed of the image
= 6 m/s + 6 m/s
= 12 m/s

### Conclusion
The velocity of the image with respect to the observer is **12 m/s**.

---