Question

A kite is 120 m 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.

Answer 1

$\mathrm{In}\mathrm{the}\mathrm{right}\mathrm{triangle}ABC,$


$$\begin{gathered} \mathrm{Here}, \\ A{B}^2+B{C}^2=A{C}^2 \\ \Rightarrow x^2+{\left(120\right)}^2=y^2 \\ \Rightarrow 2x\frac{dx}{dt}=2y\frac{dy}{dt} \\ \Rightarrow \frac{dy}{dt}=\frac{x}{y}\frac{dx}{dt} \\ \Rightarrow \frac{dy}{dt}=\frac{50}{130}\times 52\left[\because x=\sqrt{{\left(130\right)}^2-{\left(120\right)}^2}=50\right] \\ \Rightarrow \frac{dy}{dt}=20\mathrm{m}/\sec \end{gathered}$$