Question

a street light is mounted at the top of a 15-ft-tall pole. a man 6 feet tall walks away from the pole with a speed of 7 ft/s along a straight path. how fast (in ft/s) is the tip of his shadow moving when he is 40 feet from the pole? ft/s

Answer 1

35/3 ft/s.

Explanation:

Let the distance of the man from pole be x feet and the distance of the tip of the shadow be y feet , then by similar triangles:

(y - x) / y = 6/15

15y - 15x = 6y

9y = 15x

y = (5/3)x

Differentiate both sides with respect to time t:

dy/dt = (5/3) dx/dt

The man is travelling at 7 ft/s away from the wall,

that is dx/dt = 7 ft/s

So, dy/dt = 5/3 * 7 = 35/3 ft/s

Note - his distance from the pole does not matter as only the man's speed effects the speed of the tip of the shadow.