Aman of height 1.2 meters walk away from a 5-meter lamppost at a speed of 2.8 m/s. find the rate at which his shadow is increasing in length.

Let d be initial distance the man is from the lamp.
Let x(t) be length of shadow at time t.
The distance traveled is speed*time or 2.8t.

Now set up a proportion between 2 triangles.
One formed by end of shadow and top/bottom of lamp.
Small one formed by end of shadow and top/bottom of man.



Take derivative to find rate that x(t) is increasing.