Mirror Physics Help: Walking Towards a Mirror at 7 m/s

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When walking towards a mirror at 7 m/s, both you and your image approach each other at a combined speed of 14 m/s, since the image moves towards you at the same speed you are moving towards it. If you are 100 meters away from the mirror, your image is effectively 100 meters away on the opposite side, totaling 200 meters between you and your image. The initial assumption that the speed is just 7 m/s is incorrect because it does not account for the movement of the image. Understanding the mirror's reflection helps clarify the distances involved. The key takeaway is that the relative speed between you and your image is double your walking speed.
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Homework Statement


If you are walking towards a mirror at 7 m/s, how fast are you and your image approaching each other? Answer in m/s.


Homework Equations


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The Attempt at a Solution


I'm not sure how to solve this mathmatically but when I first looked at this question, I just automatically thought that the answer should be 7 m/s. Why or why not is that correct?
 
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