A man 2 metres high walks at a uniform speed of 6 km/hr away from a lamp-post 6 metres high. Find the rate at which the length of his shadow increases.

Explanation

`frac{A B}{C D}=frac{A E}{C E}`


`Rightarrow frac{6}{2}=frac{x+y}{y}`


`Rightarrow frac{x}{y}=frac{6}{2}-1=2`


`Rightarrow frac{d y}{d t}=frac{1}{2} frac{d x}{d t}`


`Rightarrow frac{d y}{d t}=frac{1}{2}(6)`


`Rightarrow frac{d y}{d t}=3 {km} / {hr}`