A street light is at the top of a 20 foot tall pole. A 6 foot tall woman walks away from the pole with a speed of 7 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 50 feet from the base of the pole?

Answer 1

If the shadow has length s
and the woman is x feet from the pole, then
s/6 = (s+x)/20
s = 3/7 x
so, ds/dt = 3/7 dx/dt = 3
So, the tip of the shadow moves at 7+3 ft/s