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  • 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}.

A car is moving at a constant speed of 60\; km\; h^{-1} on a straight road. Looking at the rearview mirror, the driver finds that the car following him is at a distance of 100 m and is approaching at 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 every 2s 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 rearview 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.

Answers (1)

The answer is the option (d).

Explanation:-

 When an object is placed in front of a mirror, all the positions of objects in the front of a mirror, image are virtual, erec,t and smaller in size. As the object moves toward the pole, magnification increases and tends to unity at the pole.

An object moving along the principal axis – on differentiating the mirror formula with respect to time we get,

\frac{dv}{dt}=\left ( \frac{v}{u} \right )^{2}\frac{du}{dt}=-\left ( \frac{f}{u-f} \right )^{2}\frac{du}{dt}

Where \frac{dv}{dt} is the velocity of the image moving along the principal axis, and \frac{du}{dt} is the velocity of the object along the principal axis.

The negative sign indicates that the image always moves in the direction opposite to that of the object

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infoexpert23

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