a man 6ft tall walks at the rate of 5ft/sec toward a streetlight that is 16ft above the ground. At what rate is the length of his shadow changing when he is 10ft from the base of the light?
If the shadow is length y when the man is x feet from the pole, then using similar triangles,
y/6 = (x+y)/16
y = 3x/5
dy/dt = 3/5 dx/dt = 3/5 (-5) = -3
so, the shadow is shrinking at 3 ft/sec regardless of the distance from the pole.posted by Steve