Word problem using geometry

Question

A street light is at the top of a pole that is 1818 feet tall. A woman 66 ft tall walks away from the pole with a speed of 55 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 1010 ft from the base of the pole?

Answer 1

Let x is distance from base of pole. Then from similyarity we have: l/(x + l) = 6/18; l/(x + l) = 1/3; 3l = x + l;

l = x/2, where l is length of shadow.

dl/dt = 1/2dx/dt = 1/2·5ft/s = 2.5 ft/s for any x, including x = 10 ft/s