00:01
So in this question, a girl flies a kite at a height of 300 feet and the wind carrying the kite horizontally away from her at a rate of 25 feet per second.
00:13
And i want to know how fast must she let out the string when the kite is 500 feet away from her.
00:21
So let's start by drawing a picture.
00:25
So what do we have here? we have a girl that is flying a kite at a constant height of 300 feet.
00:36
Now the wind is carrying the kite horizontally away from her at a rate of 25 feet per second.
00:44
So this horizontal distance x is changing at the rate of 25 feet per second.
00:52
So i have been given that my dx, dt, is 24.
01:00
5 feet per second.
01:04
Now the question is how fast must she let out the string when the kite is 500 feet away from her? so here's why.
01:15
My goal in this question is to figure out how fast does she let out the string? what is my dydt when the kite is 500 feet away from her when the value of y is 500 feet? so i am trying to relate these rates.
01:35
I'm trying to relate dxdt and dydt.
01:40
To do that, i have to start by relating x and y without their derivatives.
01:46
To do that, i'm going to say that x squared plus 300 squared is equal to y squared by the pythagorean theorem.
01:57
Now, i'm going to take the derivative of each side with respect to t.
02:02
When i do, on the left, i just get 2x dx d t...