posted by Matt .
A street light is at the top of a 15.000 ft. tall pole. A man 6.300 ft tall walks away from the pole with a speed of 6.000 feet/sec along a straight path. How fast is the tip of his shadow moving when he is 45.000 feet from the pole?
using similar triangles, we see that if the man is x from the pole, and his shadow is s long,
(x+s)/15 = s/6.3
6.3x + 6.3s = 15s
6.3x = 8.7s
So, if x is increasing and s is increasing, then the tip of the shadow is moving at speed dx/dt + ds/dt.
Or, dx/dt (1 + 6.3/8.7)
Note that it does not matter how far from the pole the man is.