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 km h^(-1)`.
B. In the side mirror the car in the rear would appear to approach with a speed of `5 km h^(-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 step by step, we will analyze the situation involving the two cars and their speeds as perceived by the driver of the leading car.

### Step 1: Understand the speeds of the cars
- The speed of the leading car (Car A) is given as 60 km/h.
- The speed of the following car (Car B) is given as 5 km/h (approaching speed).

### Step 2: Convert speeds to a common unit
- First, we convert the speeds from km/h to m/s for easier calculations:
- Speed of Car A: \( 60 \text{ km/h} = \frac{60 \times 1000}{3600} = 16.67 \text{ m/s} \)
- Speed of Car B: \( 5 \text{ km/h} = \frac{5 \times 1000}{3600} = 1.39 \text{ m/s} \)

### Step 3: Analyze the relative speed
- The relative speed of Car B with respect to Car A when viewed in the rearview mirror is:
\[ \text{Relative speed} = \text{Speed of Car A} + \text{Speed of Car B} = 16.67 \text{ m/s} + 1.39 \text{ m/s} = 18.06 \text{ m/s} \]
- This means that in the rearview mirror, Car B appears to approach at a speed of \( 18.06 \text{ m/s} \).

### Step 4: Analyze the situation in the side mirror
- When the driver looks at the side mirror, the speed of Car B does not combine with Car A's speed because they are not in the same line of motion. Therefore, Car B appears to approach at its actual speed of 1.39 m/s.

### Step 5: Distance covered in the given time
- The initial distance between the two cars is 100 m.
- The time interval for glancing at the mirrors is 2 seconds.
- In 2 seconds, Car B will cover:
\[ \text{Distance covered by Car B} = \text{Speed of Car B} \times \text{Time} = 1.39 \text{ m/s} \times 2 \text{ s} = 2.78 \text{ m} \]
- The distance between the two cars will decrease by 2.78 m every 2 seconds.

### Step 6: Determine when Car B overtakes Car A
- To find out how long it takes for Car B to overtake Car A, we need to calculate how long it takes for Car B to cover the initial distance of 100 m at a relative speed of 1.39 m/s:
\[ \text{Time to overtake} = \frac{\text{Initial Distance}}{\text{Relative Speed}} = \frac{100 \text{ m}}{1.39 \text{ m/s}} \approx 71.94 \text{ s} \]

### Conclusion
- The driver will see the following car approaching faster in the rearview mirror (at a combined speed) and slower in the side mirror (at its actual speed).
- Therefore, the correct statement is that in the side mirror, the speed of the approaching car would appear to increase as the distance decreases.