A street light on the East Mall is at the top of a 13-foot-tall pole. A 7-foot-tall man walks away from the pole with a speed of 5 ft/sec along a straight path. How fast is the tip of his shadow moving when he is 40 feet from the base of the pole?

Here is the solution:

The distance of shadow: Ss

The distance of man: Sp

Considering the relationship of distance between man and his shadow, we get:

Ss/(Sp-Ss) = 13/7

Ss = (13/6)*Sp

We take the derivative of the equation on both side, then we get:

dSs/dt = (13/6)*(dSp/dt)

Because the man’s spend is 5 ft/sec so dSp/dt = 5 and we get dSs/dt = 65/6.