Posted by Matt on .
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?

calculus 
Steve,
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.