Question

You run away from a plane mirror at 1.80 m/s. At what speed does your image move away from you?

2.70 m/s
1.80 m/s
0.90 m/s
3.60 m/s

Answer 1

`color(blue)(3.60 m/s)`

Explanation:

An image formed from a plane mirror will be the exact distance away from the plane mirror as is the object.

This means, if you are standing `2" meters"` away from a plane mirror, your reflection, or the image produced, will stand exactly `2" meters"` away from the plane mirror as well.

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If you run away from the plane mirror at a speed of `1.80 m/s`, then your image will also run `1.80 m/s` away from the plane mirror in the opposite direction, because, again, the distance is the same.

`color(white)(------)"speed" = "distance"/"time"`

But you are asked at what speed does your image move away from you, NOT the mirror.

Since you are `color(red)"x"` amount of meters from the mirror and your image is also `color(red)"x"` amount of meters from the mirror, your image's distance from you is `color(red)"2x"`, therefore, doubled. Using the speed equation from above, if your distance doubles, with time remaining the same, then the speed would also double.

`color(white)(----)1.80 m/s xx 2 = color(blue)(3.60 m/s`