A car is moving with a constant speed of `60 km h^-1` on a straight road. Looking at the rear view mirror, the driver finds that the car following him is at a distance of `100 m` and is approaching with a speed of `5 km h^-1`. In order to keep track of the car in the rear, the driver begins to glane alternatively at the rear and side mirror of his car after every `2 s` till the other car overtakes. If the two cars were maintaining their speeds, which of the following statement (s) is/are correct ?

Options

A. The speed of the car in the rear is 65 `kmh^(-1)`
B. In the side mirror, the car in the rear would appear to approach with a speed of 5 `kmh^(-1)` to the driver of the leading car
C. In the rear view mirror, the speed of the approaching car would appear to decrease as the distance between the cars decreases
D. In the side mirror, the speed of the approaching car would appear to increase as the distance between the cars decreases

Explanation

To solve the problem, we need to analyze the situation step by step.

### Step 1: Identify the speeds of both cars
The speed of the leading car (the car driven by the driver) is given as:
- Speed of leading car, \( v_1 = 60 \, \text{km/h} \)

The speed of the following car is given as:
- Speed of following car, \( v_2 = 5 \, \text{km/h} \)

### Step 2: Convert speeds to the same unit
To make calculations easier, we convert the speeds from km/h to m/s:
- \( v_1 = 60 \, \text{km/h} = \frac{60 \times 1000}{3600} = 16.67 \, \text{m/s} \)
- \( v_2 = 5 \, \text{km/h} = \frac{5 \times 1000}{3600} = 1.39 \, \text{m/s} \)

### Step 3: Calculate the relative speed
The relative speed of the following car with respect to the leading car is:
- Relative speed, \( v_{rel} = v_1 - v_2 = 16.67 \, \text{m/s} - 1.39 \, \text{m/s} = 15.28 \, \text{m/s} \)

### Step 4: Calculate the time taken to overtake
The initial distance between the two cars is \( 100 \, \text{m} \). To find the time taken for the following car to overtake the leading car, we can use the formula:
- Time, \( t = \frac{\text{Distance}}{\text{Relative Speed}} = \frac{100 \, \text{m}}{15.28 \, \text{m/s}} \approx 6.54 \, \text{s} \)

### Step 5: Analyze the statements
Now we will analyze each statement provided in the question:

1. **Statement A**: The speed of the car in the rear is \( 65 \, \text{km/h} \).
- This statement is incorrect because the speed of the following car is \( 5 \, \text{km/h} \).

2. **Statement B**: In the side mirror, the car in the rear would appear to approach with a speed of \( 5 \, \text{km/h} \) to the driver of the leading car.
- This statement is incorrect because the speed of the following car relative to the leading car is \( 15.28 \, \text{m/s} \) (or \( 55.28 \, \text{km/h} \)).

3. **Statement C**: In the rear view mirror, the speed of the approaching car would appear to decrease as the distance between the cars decreases.
- This statement is correct. As the following car approaches, the image in the rear view mirror appears to move slower due to the relative motion.

4. **Statement D**: In the side mirror, the speed of the approaching car would appear to increase as the distance between the cars decreases.
- This statement is incorrect. The speed would not appear to increase; it would appear to decrease as the distance reduces.

### Conclusion
The only correct statement is **Statement C**.