Rashdan, on Oct 10 2008, 12:25 AM, said:
I think I'll need a picture to confirm, but I'll try to answer it anyways.
Think of it like a right angled triangle. The hypotenuse is the length of the cable. The height is 12ft, which remains constant throughout. Then comes the horizontal distance (from the dock to the boat), which also changes.
Now, you know that z^2 = x^ + y^2 (where x is the horizontal distance, y is the vertical distance, z is the length of the cable. Not that y^2 is constant).
Differentiate the above in terms of TIME.
2z*dz/dt = 2x*dx/dt + 0 (as per chain rule). The 0 comes from differentiating a constant.
You know dz/dt = 4ft/s. You know z = 13ft. You know x (you can calculate it when z = 13, y = 12, using pythagoras). The only thing you don't know is dx/dt, which is what you want to find.
Classic related rates problem.
e: I assumed that it looks like a triangle, but I would like a diagram to confirm. You should just draw it on ms paint, roughly, I don't need an exact one.
e2: oops, mixed up horizontal and vertical.
Ah okay, got it. Thanks a lot. And, by the way, the diagram was a right triangle
and exactly how you explained what you thought it would look like.
One question comes to mind though. Why did the y become 0?
Edit: Wait, I think I got it. Is it because when you plug in 12 for y, you get 144. Then the derivative of 144 is 0. Is that right?
Edited by Mahmoud, 10 October 2008 - 03:44 PM.