A man 6 feet tall walks at a rate of 5 feet/sec toward a street lamp that is 16 feet above the ground. At what rate is the tip ,of his shadow moving? At what rate is the length of his shadow changing when he is 10 feet from the base of the lamp post?

Answer 1

draw a diagram. using similar triangles, if the length of the shadow is x, and the distance to the lamp is y,

x/6 = (x+y)/16
16x = 6x + 6y
10x = 6y
x = 3/5 y

since y is changing at -5ft/sec
x is changing at -3ft/sec

no matter where the man is.