A light is placed on the ground 30 ft from a building. A man 6 ft tall walks from the light toward the building at the rate of 5 ft/sec. Find the rate at which the length of his shadow is changing when he is 15 ft from the building.

Question

A light is placed on the ground 30 ft from a building.  A man 6 ft tall walks from the light toward the building at the rate of 5 ft/sec.  Find the rate at which the length of his shadow is changing when he is 15 ft from the building.

Steve · Answer

using similar triangles, when the man is x feet from the building, s/30 = 6/(30-x) 1/30 ds/dt = -6/(30-x)^2 dx/dt Now just plug in your numbers to find ds/dt