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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?
Options
The speed of the car in the rear is 65 km h–1.
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.
In the rear view mirror the speed of the approaching car would appear to decrease as the distance between the cars decreases.
In the side mirror, the speed of the approaching car would appear to increase as the distance between the cars decreases.
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Solution
In the side mirror, the speed of the approaching car would appear to increase as the distance between the cars decreases.
Explanation:
Object moving along the principal axis: On differentiating the mirror formula with respect to time, we get `(dv)/(dt) = - (v/u)^2 (du)/(dt) = - (f/(u - f))^2. (du)/(dt)`. where `(dv)/(dt)` is the velocity of image along the principal axis and `(du)/(dt)` is the velocity of object along the principal axis. A negative sign implies that the image, in case of mirror, always moves in the direction opposite to that of the object.
As the distance between the cars decreases, the speed of the image of the car would appear to increase.
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