# 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

May 23, 2017

$\textcolor{b l u e}{3.60 \frac{m}{s}}$

#### 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 $2 \text{ meters}$ away from a plane mirror, your reflection, or the image produced, will stand exactly $2 \text{ meters}$ away from the plane mirror as well. If you run away from the plane mirror at a speed of $1.80 \frac{m}{s}$, then your image will also run $1.80 \frac{m}{s}$ away from the plane mirror in the opposite direction, because, again, the distance is the same.

$\textcolor{w h i t e}{- - - - - -} \text{speed" = "distance"/"time}$

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

Since you are $\textcolor{red}{\text{x}}$ amount of meters from the mirror and your image is also $\textcolor{red}{\text{x}}$ amount of meters from the mirror, your image's distance from you is $\textcolor{red}{\text{2x}}$, 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