A street light is at the top of a 17 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 6 ft/sec. How fast is the tip of her shadow moving when she is 50 ft from the base of the pole.

Answer 1

Let her distance from the pole be x ft
let the length of her shadow at that moment be y ft

by ratio:
17/(x+y) = 6/y
17y = 6x+6y
11y = 6x

11 dy/dt = 6 dx/dt

dy/dt = 6(6)/11 = 36/11 ft/s

The tip of her shadow is moving at
dy/dt + dx/dt
= 36/11 + 6
= 102/11 or appr 9.27 ft/s

notice that this is independent of where she is, that is the 50 ft did not even enter the picture.