Question

A girl flies a kite at a height of 300 ft, the wind carrying the kite horizontally away from her at a rate of 20 ft/sec. How fast must she let out the string when the kite is 600 ft away from her

Answer 1

Answer:

$10\sqrt3 ft/s$

Step-by-step explanation:

We are given that

Height of kite from ground=300 ft

In triangle ABC,

AB=300 ft

Let BC=h ft , AC=y=600 ft

$\frac{dh}{dt}=20 ft /s$

We have to find the rate at which she must let out the string when the kite is 600 ft away from her.

By pythagorous theorem

$(300)^2+h^2=(600)^2$

$90000+h^2=360000$

$h^2=360000-90000=270000$

$h=300\sqrt3 ft$

$(300)^2+h^2=y^2$

Differentiate w.r.t t

$2h\frac{dh}{dt}=2y\frac{dy}{dt}$

$h\frac{dh}{dt}=y\frac{dy}{dt}$

Substitute the values then we get

$300\sqrt3\times 20=600\times \frac{dy}{dt}$

$\frac{dy}{dt}=\frac{300\sqrt3\times 20}{600}=10\sqrt3 ft /s$

Hence, she must let out the string at the rate $10\sqrt3 ft/s$ when the kite is 600 ft away from her.