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