Monday

September 1, 2014

September 1, 2014

Posted by **Monique** on Tuesday, September 20, 2011 at 7:24pm.

- Geometry -
**Reiny**, Tuesday, September 20, 2011 at 8:00pmA much more difficult question than it appears.

A cable would hang in the form a catenary, from the Latin catena = chain

the general equation of a catenary is

y = (a/2)( e^(x/a) + e^(-x/a)

so imagining our cable on the x-y grid,

the lowest point would then be (0,5) giving us

5 = (a/2)(1 + 1)

a = 5

so the equation is y = (5/2)(e^(x/5) + e^(-x/5))

the end points are (x,20) and (-x,20)

sub in y = 20

20 = (5/2)(e^(x/5) + e^(-x/5))

8 = e^(x/5) + e^(-x/5)

Nasty equation to solve, lately I have been using Wolfram to solve such difficult equations.

http://www.wolframalpha.com/input/?i=e%5E%28x%2F5%29+%2B+e%5E%28-x%2F5%29+%3D+8

it gave as solutions x = 5ln(4+√15) and x = 5ln(4-√15)

5ln(4+√15) = appr. 10.317

so the distance between them is 2(10.317) = 20.63 ft

The fact that the cable is 30 ft long appears to be redundant information.

One would need to use integral calculus and the formula for the "length of a curve" to show that it is actually 30 feet.

- Geometry -
**Reiny**, Tuesday, September 20, 2011 at 8:57pmI looked at this question again, because I thought that I was "overthinking" it.

I think the problem is flawed.

Suppose the two poles are flush against each other, then the chain would reach 15 feet down each of the poles, that is, it would end up 5 feet above the ground.

As soon as the poles are pulled apart, the lowest point of 5 feet would then rise.

So for the given data of the cable being 30 feet, the distance between the two poles would have to be zero.

**Answer this Question**

**Related Questions**

geometry - A 30-foot cable is suspended between the tops of two 20-foot poles on...

Geometry - A 30-foot cable is suspended between the tops of two 20-foot poles ...

Geometry - A 30-foot cable is suspended between the tops of two 20-foot poles on...

Calculus - A cable hangs between two poles of equal height and 40 feet apart. At...

Calculus - A cable is suspended from two towers with a distance of 100m between ...

Applied Calculus - An underground electricity cable is to be laid between two ...

IT - If I have a steel cable pulling 5 degrees from straight down by 1500lbs. ...

math(Please help!!!) - A cable that is used to support a 76 foot tower is ...

trigonometry - A tent pole is 85 feet high. A cable is attached to the ground ...

math - There are two 100-foot poles. A 150-foot rope connects them at the top. ...