An object is moving towards a stationary plane mirror with a speed of 2 m/s. Velocity of the image w.r.t. the object is

Options

A. 2 m/s towards right
B. 4 m/s towards right
C. 2 m/s towards left
D. 4 m/s towards left

Explanation

To solve the problem of finding the velocity of the image with respect to the object when the object is moving towards a stationary plane mirror, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Motion**:
- The object is moving towards the plane mirror with a speed of 2 m/s.

2. **Identify the Velocity of the Image**:
- For a plane mirror, the image moves in the opposite direction to the object but with the same speed. Therefore, if the object moves towards the mirror at 2 m/s, the image will also appear to move towards the mirror at 2 m/s.

3. **Determine the Direction**:
- Since the object is moving towards the mirror, we can consider the direction towards the mirror as negative. Thus, the velocity of the object (v_object) can be represented as:
\[ v_{object} = -2 \, \text{m/s} \]
- The velocity of the image (v_image) will be:
\[ v_{image} = 2 \, \text{m/s} \, \text{(towards the mirror)} \]
- However, since the image is also moving towards the mirror, we can represent its velocity as:
\[ v_{image} = -2 \, \text{m/s} \]

4. **Calculate the Velocity of the Image with Respect to the Object**:
- The relative velocity of the image with respect to the object (v_image/object) can be calculated using the formula:
\[ v_{image/object} = v_{image} - v_{object} \]
- Substituting the values:
\[ v_{image/object} = (-2 \, \text{m/s}) - (-2 \, \text{m/s}) = -2 \, \text{m/s} - (-2 \, \text{m/s}) = -2 \, \text{m/s} + 2 \, \text{m/s} = -4 \, \text{m/s} \]

5. **Interpret the Result**:
- The negative sign indicates that the image is moving towards the left with respect to the object. Thus, the velocity of the image with respect to the object is 4 m/s towards the left.

### Final Answer:
The velocity of the image with respect to the object is **4 m/s towards the left**.