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.

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Solution

When the object moves with speed u towards (or away) from the plane mirror then the image also moves toward (or away) with speed u. But the relative speed of image w.r.t. object is 2u.

Given, speed of car, v = 3 m/s
Since the image of the truck will travel a distance twice the distance travelled by car in equal time, therefore
speed of the object in mirror = 2v = 2(3) = 6 m/s.
Hence, the image of the truck appears to approach the driver at a speed of 6 m/s.

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