Question

A car is moving with at 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 glance 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?

• 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 decrease
• D. In the side mirror, the speed of the approaching car would appear to increase as the distance between the car decrease

Answer 1

Answer: (C)

In the rear view mirror, the speed of the approaching car would appear to decrease as the distance between the cars decrease

mirror formula:

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

differentiating both side:

$\frac{dv}{v^2}=-\frac{du}{u^2}$

$⟹\frac{dv}{du}=-\frac{v^2}{u^2}$

So when rear car approaches, initially it appear at rest as image is formed at focus. When car approaches nearer this speed will appear to increase so answer is (d)