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 7 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

Explanation:

Answer 2

Since only his speed affects how fast his shadow moves, then we calculate for the speed which is 11.67ft/s

Explanation:

Assuming similar triangle

(y-x)/y = 6/15

15(y-x) = 6y

15y - 15x = 6y

(15 -6)y = 15x

9y = 15x

y = (5/3)x

By differentiating both sides with respect to time t

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

But (dx/dt) is 7 ft/s

Therefore dy/dt = 5/3 * 7 = 35/3 = 11.67ft/s