A person whose height is 6 feet 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 a streetlight is 15 feet, what is the rate at which a person's shadow is lengthening?

Question

Mathematics

Veronica Singleton

20 May, 19:38

A person whose height is 6 feet 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 a streetlight is 15 feet, what is the rate at which a person's shadow is lengthening?

+1

Answers (1)

Know the Answer?

Ernesto Skinner · Answer 1

Let the distance from the pole be x and the length of the shadow be s. Using the law of similar triangles, we have:

s/6 = (x+s) / 15

thus

5s=2x+2s

3s=2x

hence

ds/dt=2/3 dx/dt

but

dx/dt=4 ft per second

hence

ds/dt=2/3*4=8/3