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

\[\text { In the right triangle ABC },\]

\[\text { Here,} \]

\[A B^2 + B C^2 = A C^2 \]

\[ \Rightarrow x^2 + \left( 120 \right)^2 = y^2 \]

\[ \Rightarrow 2x\frac{dx}{dt} = 2y\frac{dy}{dt}\]

\[ \Rightarrow \frac{dy}{dt} = \frac{x}{y}\frac{dx}{dt}\]

\[ \Rightarrow \frac{dy}{dt} = \frac{50}{130} \times 52 \left[ \because x = \sqrt{\left( 130 \right)^2 - \left( 120 \right)^2} = 50 \right]\]

\[ \Rightarrow \frac{dy}{dt} = 20 m/\sec\]