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?

Answer 1

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.