Why Does the Image in a Rear View Mirror Appear to Approach at Double the Speed?

[Aditya3003]

Homework Statement

The rear view mirror of a car is a plane mirror. A driver is reversing his car at a speed of 2m/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?

The Attempt at a Solution

This question was given in 2 of my books and the answer is 4m/s.How is this possible?I think it should be 2m/s.Please try to give mathematical answers.

The Attempt at a Solution

 

[Basic_Physics]

I tend to agree with you. Look at it this way - the problem would be the same if the car was stationary and the truck was approaching at 2 m/2. At all stages of the motion of the truck the image will be the same distance behind the mirror as the truck is behind the car, giving the image the same speed as the approaching truck with respect to the car.

 

[Aditya3003]

My books are definitely wrong. If you are approaching the mirror or going away from it the speed would be doubled.But in this case the distance is not doubled because the distance between us and the image is there.

 

[CWatters]

I agree with you = 2m/s.

Some sites say 2m/s, others 4m/s and one in India even says 8m/s but offers no explanation.

For what it's worth one explanation for 4m/s went something like this (I paraphrase)..

At anyone time the car and truck are distance D apart. However the image of the truck appears to be distance D in front of the car. This means the distance from the truck to the image of the truck is 2D. When the car reaches the truck the distance between truck and image of truck should approach zero. Therefore the image must appear to move twice as fast as the car.

I believe that's wrong because they forget to subtract the velocity of the car/driver. The image of the truck is moving at 4m/s w.r.t the truck but only 2m/s w.r.t the car and driver.