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  4. A kite is 300 m high and there are 500 m of cord out. If the wind moves the kite horizontally at the rate of 5 km / hr. directly away from the person who is flying it, the rate at which the cord is being paid is

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Q. A kite is $300\, m$ high and there are $500\, m$ of cord out. If the wind moves the kite horizontally at the rate of $5\, km / hr$. directly away from the person who is flying it, the rate at which the cord is being paid is

Application of Derivatives

Solution:

image
From figure $z^2=x^2+y^2$
$z \frac{d z}{d t}=x \frac{d x}{d t}$
If $z=500$ then $x=400$
$\Rightarrow 500 \frac{ dz }{ dt }=400(5) $
$\Rightarrow \frac{ dz }{ dt }=4$