A man 160 cm tall, walks away from a source of light situated at the top of a pole 6m high at the rate of 1.1 m/sec. How fast is the length of his shadow increasing when he is 1 metre away from the pole.

Explanation

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


`Rightarrow frac{6}{1.6}=frac{x+y}{y}`


`Rightarrow frac{x}{y}=frac{6}{1.6}-1`


`Rightarrow frac{x}{y}=frac{4.4}{1.6}`


`Rightarrow y=frac{16}{44} x`


`Rightarrow frac{d y}{d t}=frac{16}{44}(frac{d x}{d t})`


`Rightarrow frac{d y}{d t}=frac{16}{44} times 1.1(because frac{d x}{d t}=1.1)`


`Rightarrow frac{d y}{d t}=0.4 m / {sec}`