Question

a man 2 meters tall walks at a rate of 1.2 meters per second away from a light that is 5 meters above the ground.

(a) when he is 3m from the base of the light, at what rate is the tip of his shadow moving?
(b) when he is 3m from the base of the light, at what rate is the length of his shadow changing?

Answer 1

If the shadow has length s, then when the man is x meters from the spot below the light,
s/2 = (x+s)/5
s = 2/3 x
(b) ds/dt = 2/3 dx/dt = 2/3 * 6/5 = 4/5 m/s
(a) ds/dt + dx/dt = 4/5 + 6/5 = 2 m/s