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

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Homework Help Overview

The problem involves a driver reversing a car and observing the image of a parked truck in a plane rear view mirror. The question centers on the perceived speed of the truck's image as it approaches the driver, with conflicting answers suggesting it could be either 2m/s or 4m/s.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relationship between the speed of the car and the perceived speed of the image, with some suggesting that the image's speed should match the truck's speed relative to the car. Others question the reasoning behind the doubling of speed and the implications of distance in the scenario.

Discussion Status

The discussion is ongoing, with various interpretations being explored. Some participants express agreement on certain points, while others challenge the reasoning and calculations presented. There is no clear consensus on the correct perceived speed of the image.

Contextual Notes

Participants note discrepancies in textbook answers and the lack of clear explanations from various sources. The discussion highlights the complexity of interpreting motion in relation to mirrors and relative speeds.

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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

 
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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.
 
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.
 
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.
 

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