"A man of height 2.2 meters walk away from a 5-meter lamppost at a speed of 1.2 m/s. Find the rate at which his shadow is increasing in length. " what is the answer to this? if anyone can help that would be great

Answer 1

If the shadow has length s, then when the man is x meters from the pole, using similar triangles,

s/2.2 = (x+s)/5
5s/11 = s/5 + x/5
25s = 11s + 11x
14s = 11x
s = (11/14)x

that means that

ds/dt = (11/14) dx/dt = (11/14)(6/5) = 22/25 = 0.88 m/s

It does not matter how far away from the pole the man is. His shadow is always a constant multiple of his distance from the pole.