A kit is 120m high and 130 m of string is out. If the kite is moving away horizontally at the rate of 52 m/sec, find the rate at which the string is being paid out.

Explanation

`A B^{2}+B C^{2}=A C^{2}`


`Rightarrow x^{2}+(120)^{2}=y^{2}`


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


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


`Rightarrow frac{d y}{d t}=frac{50}{130} times 52[because x=sqrt{(130)^{2}-(120)^{2}}=50]`


`Rightarrow frac{d y}{d t}=20 m / {sec}`