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

1 Answer
Maxwell
May 23, 2017

#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.

http://www.edu.pe.ca/gray/class_pages/krcutcliffe/physics521/17reflection/definitions/17%20definitions%20how%20point%20seen%20in%20mirror.htm

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#

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