A street light is at the top of a 16 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 40 ft from the base of the pole?

Answer 1

L = pole to shadow tip
x = pole to walker
so (L-x) = walker to shadow tip
L/16 = (L-x)/6 (similar triangles)
6 L = 16 L - 16 x

16 x = 10 L
L = 1.6 x
dL/dt = 1.6 dx/dt