Question

A person whose height is 6 feet is walking away from the base of a streetlight along a straight path at 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. Let the distance from the pole be x, and the shadow's length be s. Using similar triangles, we have

s/6 = (x+s)/15
or,
5s = 2x+2s
3s = 2x

so,

ds/dt = 2/3 dx/dt

plug and chug

Answer 2

utr