A street light is at the top of a 15 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 5 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 50 ft from the base of the pole?

5 answers

Did you make a sketch?

I called her distance from the pole x ft, and the length of her shadow y ft
So by similar triangles,
6/y = 15/(x+y)
15y = 6x + 6y
9y = 6x
3y = 2x

3dy/dt = 2dx/dt
we know that dx/dt = 5
3dy/dt = 10
dy/dt = 10/3 ft/sec

So her shadow is increasing at 10/3 ft/sec
BUT, her shadow is moving along with her speed of 5 ft/sec, so
the end of her shadow is moving at 5 + 10/3
or 25/3 ft/s

(that last part is the trick-part of this question)

15 ft 3 dy

15 ft

2 ps