(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Problem is regarding approximating the value of a in y= a cosh(x/a) using Newton's method, and then use a to find the length of the rope.

That equation represents the curve formed by a rope hanging with it's ends attached to poles at a distance 2b.

(cosh() = hyperbolic cosine)

distance between poles = 2b = 400 ft.

sag = S = 30 ft.

2. Relevant equations

(previously proven eqns)

L = 2 a sinh(b/a)

where L is the length of the rope

a is a physical constant

and 2b is the distance between the poles that the rope is hanging from

S = a cosh(b/a) - a

where S is the sag (vertical distance between highest and lowest points on the rope)

a is a physical constant

2b is distance between poles

3. The attempt at a solution

I am really not sure how to do this, as I do not know how/why Newton's method could be used to get a value for a.

Also, they gave a hint, a clip from the Calc book I am reading: "[Hint: First let u = 200/a]"

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# Homework Help: Catenary - rope hanging between poles

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