The rear view mirror of a car is a plane mirror. A driver is reversing his car at a speed of 2m/s. The driver sees in his rear view mirror the image of truck parked behind his car. The speed at which of the image of the truck appears to approach the driver will be

Options

A. 1m/s
B. 2m/s
C. 4m/s
D. 8m/s

Explanation

To solve the problem, we need to determine the speed at which the image of the truck appears to approach the driver when he is reversing his car.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- The driver is reversing his car at a speed of 2 m/s.
- The truck is parked behind the car, and its image is seen in the rear view mirror, which is a plane mirror.

2. **Image Formation in a Plane Mirror**:
- In a plane mirror, the distance of the image from the mirror is equal to the distance of the object from the mirror.
- If the car moves away from the mirror, the image of the truck will appear to move towards the driver.

3. **Calculating the Relative Speed**:
- When the driver reverses the car at 2 m/s, the distance between the car and the truck decreases.
- Since the image of the truck is at the same distance behind the mirror as the truck is in front of the mirror, the image will also appear to approach the driver at the same rate.

4. **Total Approach Speed**:
- The speed at which the image of the truck approaches the driver is the sum of the speed of the car and the speed of the image.
- Since the image moves towards the driver at the same speed as the car is moving away from the mirror, the image appears to approach at a speed of 2 m/s (the speed of the car) + 2 m/s (the speed of the image) = 4 m/s.

5. **Final Answer**:
- Therefore, the speed at which the image of the truck appears to approach the driver is **4 m/s**.