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nata0808 [166]
3 years ago
12

Electrical wires suspended between two towers form a catenary (see figure) modelled by the equation shown below, where x and y a

re 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.)

Physics
1 answer:
RideAnS [48]3 years ago
8 0
Given that the arc length is:
s = ∫ √[1² + (dy/dx)²] dx 

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

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

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