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 truck parked behind his car. This speed at which the image of the truck appears to approach the driver will be? If the truck is 20m behind the car, after how long will the car crash into the truck? [5 MARKS]

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Solution

Concept : 2 Mark
Speed of Truck : 1.5 Marks
Time : 1.5 Marks

The speed of car is 2 m/s which means the car is approaching the truck with a speed of 2 m per second. The distance between the image of truck and truck will decrease at a double rate. This happens because for each meter the car moves, the mirror becomes closer to the object by 1 meter and also the image becomes 1 meter closer.
This is because the image of the truck will travel a distance twice the distance travelled by the car in equal time. Hence, the image of the truck will appear to approach the driver with the speed of 2 × 2 = 4 m/s.

Since the distance between the truck and car is 20m and the car is going back at a speed of 2m per second, the car will hit the truck in 10 seconds.

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