Question

A kite is moving horizontally at a height of 151.5 m. If the speed of the kite is 10 m/s, how fast is the string being let out, when the kite is 250 m from the boy who is flying the kite, the height of the boy being 1.5 m?

• A. 4 m/s
• B. 8 m/s
• C. 16 m/s
• D. 32 m/s

Answer 1

The correct option is B 8 m/s

Let the position of the kite at time t be at C.
$\therefore BC=151.5m$
Let AD be the boy who is flying the kite.
Let AB = x = DE and DC = y
$\therefore CE=BC-BE=151.5-1.5=150m$
Now, in $\Delta CDE$,
$y^2=x^2+(150{)}^2$
$\Rightarrow 2y\frac{dy}{dt}=2x\frac{dx}{dt}\Rightarrow \frac{dy}{dt}=\frac{x}{y}.\left(10\right)(\because \frac{dx}{dt}=10m/s)=\frac{10\sqrt{y^2-(150{)}^2}}{y}=\frac{10\sqrt{(250{)}^2-(150{)}^2}}{250}=\frac{10\times 200}{250}=8m/s$