# Thread: Help with Word Problem

1. ## Help with Word Problem

A kite is flying 100 feet above ground at the end of a string 125 feet long. The girl flying the kite lets out the string at the rate of one foot per second. If the kite remains 100 feet above ground, how fast is its horizontal distance from the girl increasing?

I haven't the foggiest idea how to even start this. Any help is appreciated.

2. Originally Posted by JonathanEyoon
A kite is flying 100 feet above ground at the end of a string 125 feet long. The girl flying the kite lets out the string at the rate of one foot per second. If the kite remains 100 feet above ground, how fast is its horizontal distance from the girl increasing?

I haven't the foggiest idea how to even start this. Any help is appreciated.
Start the same way you start any related rates problem. draw a diagram. label your unknowns as variables and your constants on the diagram. Then, think of a formula that relates all your unknowns together. Then you can differentiate implicitly and all that jazz.

here is the diagram:

can you continue?

3. MmMm... Would we use the Pythagorean Formula?

a^2 + b^2 = c^2

If so, how would I proceed? We just started this stuff and i'm so lost

4. Originally Posted by JonathanEyoon
MmMm... Would we use the Pythagorean Formula?

a^2 + b^2 = c^2

If so, how would I proceed? We just started this stuff and i'm so lost
yes, that's what you would use. why are you lost? what would a, b and c be in your problem here? just plug them in and continue

5. so we just plug in 125 for a, 100 for b and we find c? And that'll be the answer?

6. Originally Posted by JonathanEyoon
so we just plug in 125 for a, 100 for b and we find c? And that'll be the answer?
if it was that easy, this would be a middle school math problem.

this is a related rates problem. don't you think you would have to differentiate at some point? how are you going to find the rate? look at what the problem asked for

7. lol thought that would've been too easy. MmMm....Well i'm having trouble how to knowing which one is which in labeling dx/dt, dy/dt and anything else that comes into play with these kinds of problems. How am I supposed to know which one is which? Maybe I can pull through once I have an understanding of that.

8. Originally Posted by JonathanEyoon
lol thought that would've been too easy. MmMm....Well i'm having trouble how to knowing which one is which in labeling dx/dt, dy/dt and anything else that comes into play with these kinds of problems. How am I supposed to know which one is which? Maybe I can pull through once I have an understanding of that.
what do you mean how do you know? i labeled them on my diagram. y is the hypotenuse, x is the base of the triangle, 100 is the height. dy/st and dx/dt are the rates at which the hypotenuse and base are changing respectively

9. could you guide me through the next step?

I still have no idea how to set up the problem. I'm looking at the textbook at a similar problem and it is using dx/dt and dy/dt into the Pythagorean formula without giving reason why. Why are we incorporating that?