A car is moving with at a constant speed of 60 𝑘𝑚/ ℎ 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 . 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?

Open in App

Solution

The formulas of relative motion for plane mirrors are not applicable in this case.
So, options (𝑎) and (𝑏) are not correct.
As we know, mirror formula is given by,

\(\dfrac{1}{f}=\dfrac{1}{v}+\dfrac{1}{u}\)

differentiating both side we get,

\(\dfrac{dv}{v^2}=-\dfrac{du}{u^2}\)

\(\dfrac{dv}{du}=-\dfrac{v^2}{u^2}\)

So, when car approaches nearer, this speed will appear to increase.

Final Answer: (𝑑)

Suggest Corrections

Similar questions

Q. The rear view mirror of a car is a plane mirror. A driver reverses his car at a speed of 3 m/s. The driver sees in his rear view mirror, the image of a truck approaching behind his car. Find the speed at which the image of truck appears to approach the driver.

Question 13
The rear view mirror of a car is a plane mirror. A driver is reversing his car at a speed of 2 m/s. The driver sees in his rear view mirror the image of a truck parked behind his car. The speed at which the image of the truck appears to approach the driver will be
(i) 1 m/s
(ii) 2 m/s
(iii) 4 m/s
(iv) 8 m/s

Q. A car is moving with at a constant speed of 60 km