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.

Answer 1

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