Yes, I used co-ordinate geometry.
I let the centre point between the two poles be (0,0)
And I let the bottom of one pole be (-b,0) and the other be (b,0)
This shape is a catenary.
The formula for a catenary is
\(\boxed{y=c+acosh(\frac{x}{a})\\ where\\ cosh(x) =\frac{e^x+e^{-x}}{2}}\)
The arclength of this section of catenary is L which is 80m
It can be shown that:
\(L=\displaystyle\int_{-b}^{b}\;\sqrt{1+\left(\frac{dy}{dx}\right)^2}\;dx\)
Put all this together and I ended up getting either nonsense or that b/a=0
It was then that I looked at the question properly and had my Doh! moment.
All suspended ropes, chains etc hang in a catenary.
There are a lot of good youtube clips available if you want to look at them.
