# Hanging cable problem

#### soroban

##### Well-known member

The ends of an 80-foot cable are attached to the tops of two 50-foot pole.
The lowest point of the cable is 10 feet from the ground.
Find the distance between the poles.

Code:
                L = 80
*                 *
|                 |
|                 |
|*               *|
|                 |
50 | *             * | 50
|  *           *  |
|    *       *    |
|        *        |
|        :        |
|        :10      |
|        :        |
*--------+--------*
: - - -  x  - - - :
The equation of a hanging cable is not a parabola.

It is a catenary, with the basic equation: .$$y \:=\:\frac{e^{ax} + e^{-ax}}{2}$$

[There is a reason why this problem is not
. . listed under "Challenge Questions".]

Last edited:

#### kanderson

##### Member
This is what I used to get my bridge design lol. I had to write a paper on this. Wish I could find it on my school computer and give it to you guys. Here is a mathematician from oxford that is inspiring and talks about catenary The Catenary - Mathematics All Around Us. - YouTube Although not an explanation more like trying to get people to see something in mathematics, here is one that explains catenary curve The Catenary - YouTube .

#### Opalg

##### MHB Oldtimer
Staff member
I'm thinking, what happens when the poles get closer and closer together? Aha! So that's why you wrote "pole" rather than "poles", I thought it was just a typo.

#### soroban

##### Well-known member
Hello, Opalg!

You got it!

The word "pole" was indeed a typo.
I've corrected it.