Street light Calculus Problem

Question

A street light is at the top of a 20-ft-tall pole. A 6-ft tall woman walks away from the pole with a speed of 7 ft/sec along a straight path (see figure). How fast is the tip of her shadow moving, in ft/sec, when she is 35 ft from the base of the pole?

Answer 1

From similyarity of triangles: y/(x + y) = 6/20; or y/(x + y) = 3/10; 10y = 3x + 3y; 7y = 3x; y = 3/7x.

Here x is distance from woman to pole, y is length of shadow. We differentiate: y' 3/7x' = 3/7·7ft/s = 3 ft/s.

So, tip of shadow independent of distance x and always 3 ft/s