Question

Electrical wires suspended between two towers form a catenary (see figure) modelled by the equation shown below, where x and y are measured in meters. y = 20 cosh(x/20) ?20 ? x ? 20 The towers are 40 meters apart. Find the length of the suspended cable. (Round your answer to three decimal places.)

Answer 1

Given that the arc length is:
s = ∫ √[1² + (dy/dx)²] dx

So arc length between the two points is then:
s = 2*20sinh(x/20)
= 40sinh(x/20)

The straight distance between the two points is : d = 2x
So, x = d/2.
= 40/2
= 20 m

Plug this into the arc length equation to get:
s = 40sinh[20/20)]
=40* ½ (e - 1/e)
= 47 m