Question

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 30 ft from the pole?

Answer 1

Answer: 2.67 ft/s

Explanation:

1) The diagram with the triangle that represents the situation is in the image attached.

2) Similarity properties

(x + y) / 15 = y/6

⇒ 6(x+y) = 15y

⇒ 6x + 6y = 15y

⇒ 6x = 15y - 6y

⇒ 6x = 9y

⇒ y = 6x / 9

⇒ y = 2x / 3

3) Velocity is the derivative respecto to time. Then, find the derivative respect to time, t, on both sides

dy/dt = (2/3)dx/dt

4) The statement tells v = dx/dt = 4 ft/s

⇒ dy/dt = (2/3) 4 ft/s = (8/3)m/s ≈ 2.67 ft/s

Notice that this speed is constant, it does not depends upon the distance of 30 ft.