A person whose height is 6feet is walking away from the base of a streetlight along a straight path at a rate of 4 feet per second. If the height of the streetlight is 15 feet, what is the rate at which the person's shadow is lengthening?

Answer 1

draw a diagram. using similar triangles, when the person is x ft from the light pole,
6/s = 15/(x+s)
6(x+s) = 15s
6x = 9s
s = 2/3 x
so
ds/dt = 2/3 dx/dt
since dx/dt = 4, ds/dt = 8/3 ft/s
regardless of the distance from the light