A 5ft tall person is walking toward a light 20ft off the ground at 8 ft/sec. What is the rate of change of the length of the persons shadow when they are 15ft away from the light? What is the speed of the tip of the shadow moving?

Answer 1

using similar triangles, if the person is x feet away, and the shadow has length s,

s/5 = (x+s)/20
4s = x+s
x = 3s

so, dx/dt = 3 ds/dt
that means ds/dt = -8/3 ft/s

So, the shadow is shrinking as the man is walking, so the tip is moving at the rate of -(8 + 8/3) = -32/3 ft/s

what does the minus sign mean?