Question

A street light is mounted at the top of a 19-ft-tall pole. A man 5.5 feet tall walks away from the pole with a speed of 14 ft/s along a straight path. How fast is the tip of his shadow moving when he is 100 feet from the pole?

Answer 1

If the man is x feet from the pole, and his shadow has length s, then by similar triangles,

(x+s)/19 = s/5.5
19s = 5.5(x+s)
13.5s = 5.5x
s = .407x
The tip of the shadow is at distance x+s = 1.407x

so, it is moving with speed

d(x+s)/dt = 1.407 dx/dt
= 1.407*14 = 19.7 ft/s