# A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 4 ft/s along a straight path. How fast is the tip of his shadow moving when he is 50 ft from the pole?

##### 1 Answer

Dec 22, 2017

#### Explanation:

in this diagram, x is the distance from the man to the pole, and y is the distance from the tip of the man's shadow to the pole. i assume the man and pole are standing straight up, which means the 2 triangles are similar.

by similarity,

differentiate both sides with respect to

you know

that means

actually, the man's distance from the pole doesn't matter since only his speed affects how fast his shadow moves.