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?

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

Step-by-step 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