The rear view mirror of a car is a plane mirror. The driver can see the image of a bus parked behind his car in the rear view mirror. If the driver reverses his car at a speed of 0.75 m/s, at which speed the image of bus will appear to approach the car driver ?

Answer

To solve the problem of how fast the image of the bus will appear to approach the car driver when he reverses his car, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- The rear view mirror of the car is a plane mirror.
- The driver sees the image of a bus parked behind his car in this mirror.

2. **Identifying the Speeds**:
- The driver is reversing the car at a speed of 0.75 m/s.

3. **Understanding Image Formation in Plane Mirrors**:
- In a plane mirror, the distance of the object from the mirror (u) is equal to the distance of the image from the mirror (v). Therefore, if the object (bus) is at a certain distance behind the mirror, the image will appear at the same distance in front of the mirror.

4. **Calculating the Relative Speed**:
- As the driver reverses the car at 0.75 m/s, the mirror (and hence the driver) is moving towards the bus.
- Since the image of the bus is also moving towards the driver at the same rate, the speed at which the image of the bus appears to approach the driver is the sum of the speed of the driver and the speed of the image.

5. **Final Calculation**:
- Speed of the driver (reversing) = 0.75 m/s
- Speed of the image of the bus (approaching) = 0.75 m/s
- Total speed at which the image appears to approach the driver = Speed of the driver + Speed of the image = 0.75 m/s + 0.75 m/s = 1.50 m/s.

6. **Conclusion**:
- Therefore, the image of the bus will appear to approach the car driver at a speed of 1.50 m/s.

### Final Answer:
The image of the bus will appear to approach the car driver at a speed of **1.50 m/s**.

---