A light on the ground moving at 0.5 m/s approaches a man standing 4 m from a wall. How fast is the tip of the man’s shadow moving when the light is 10 m from the wall?

Answer 1

depends on the man's height, h. If the shadow's height is s and the light is x m from the wall, then using similar triangles, we have

x/s = (x-4)/h
x/(x-4) = s/h
-4/(x-4)^2 dx/dt = 1/h ds/dt

So, plugging your numbers,

-4/36 * -1/2 = 1/h ds/dt
ds/dt = h/18