Question

A boy is flying a kite, which is at a height of 40 feet. The kite is moving horizontally

at a rate of 3 feet per second. If the string is taut, at what rate is the string being

paid out when the length of the string released is 50 feet?

PLEASE ANSWER MY QUESTION QUICKLY!!!

DEADLINE : 05/03/2022 11 : 00 PM

Answer 1

$a^2+b^2=c^2$

Now implicitly differentiate that relationship

$2ada/dt+2bdb/dt=2c dc/dt$

b=40

c=50

da/dt=3

db/dt=o, because it is not change.

we can find "a" using the pythagorean theorem

$a^2+40^2=50^2$

$a=\sqrt{50^2-40^2}=30$

We can know plug into our differentiated equation and solve it.

$30x3=50 dc/dt$

$dc/dt=90/50=1.8 ft/sec$