A street light is at the top of a 16ft tall pole. A woman 6ft tall walks away from the pole with a speed of 6ft/sec along a straight path. How fast is the tip of her shadow moving when she is 30ft from the base of the pole?

Answer 1

If the woman is x feet from the pole, and her shadow is of length s, then

s/6 = (x+s)/16
s/6 = x/16 + s/16
5/48 s = x/16
s = 3/5 x

So, unlike the problem where some angle is steadily changing, here the shadow is always 3/5 as long as the distance from the pole.

Since dx/dt = 6, ds/dt = 18/5

No matter how far she is from the pole.

However, that is not the answer to the question. The tip of her shadow is moving 18/5 from the woman. Add to that her own walking speed, and we see that the tip of the shadow is moving at 18/5 + 6 = 48/5 ft/s