Question

A man 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.

Answer 1

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.


`(d+2.8t+x(t))/(x(t)) = (5)/(1.2) \\ \\ x(t) = 0.88t +0.32 d`

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

`(dx)/(dt) = 0.88`