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 30 ft from the base of the pole?

Answer 1

Let the woman be b feet from the pole, and let her shadow be a feet long.

Using similar triangles,

a/6 = (a+b)/16
so a = 3/5 b

da/dt = 3/5 db/dt = 3/5 * 4 = 12/5 ft/sec, a constant speed.

That seems odd. I expected her shadow's length to accelerate, but I don't see an error. These problems usually involve a steadily changing angle, and with the tangent function things speed up quickly. Not so here...