Question

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

• A. $2km/hr$
• B. $4km/hr$
• C. $6km/hr$
• D. $8km/hr$

Answer 1

The correct option is B $4km/hr$

$x^2+y^2=r^2$

$2x\frac{dx}{dt}+2y\frac{dy}{dt}=2r\frac{dr}{dt}$

Interchanging positions of $x$ and $y$,

$\underset{400}{\underset{\uparrow }{2x}}\underset{5km/hr}{\underset{\uparrow }{\frac{dx}{dt}}}+2y\underset{0}{\underset{\uparrow }{\frac{dy}{dt}}}=\underset{500}{\underset{\uparrow }{2r}}\underset{?}{\underset{\uparrow }{\frac{dr}{dt}}}$

$\therefore 2\times \frac{400}{1000}=2\times \frac{500}{1000}\frac{dr}{dt}$

$\frac{dr}{dt}=\frac{4}{5}\times 5$

$\frac{dr}{dt}=4km/hr$