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

Since triangles `{ABE}` and `C D E` are similar ,



`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}`