Question

A man 6.5 ft tall approaches a street light 17.0ft above the ground at the rate of 8.00 ft/s. How fast is the end of the man's shadow moving when he is 5.0 ft from the base of the light? The end of the man's shadow is moving at a rate of_ft/s

Answer 1

Draw a diagram. If the man is x feet from the pole, and his shadow has length s, then using similar triangles, we see that

s/6.5 = (x+s)/17
2s/13 = (x+s)/17
34s = 13x+13s
21s = 13x
s = 13/21 x

So,

ds/dt = 13/21 dx/dt

So, it does not matter how far away he is, his shadow's length is changing 13/21 as fast as his distance from the pole.