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.

$\frac{d+2.8t+x(t)}{x(t)} = \frac{5}{1.2} \\ \\ x(t) = 0.88t +0.32 d$

Take derivative to find rate that x(t) is increasing.
$\frac{dx}{dt} = 0.88$