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?
Accepted Solution
A:
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