Hyperbolic Functions: Catenary: Example 4: Arc Length

In this video I go over another example involving catenary telephone wires, and this time determine the formula for the length of the wire as well as calculating the required height at which they need to be hung on telephone poles. The length of the wire can be solved by using the arc length formula which I have covered before. When given the height at which the cables or wires are supposed to sag due to gravity, we can then work backwards and use the catenary formula as well as the length of the wire formula to obtain the required height at the poles. In solving this example I make use of the amazing Wolfram Alpha calculator to quickly find the solution to a pretty complicated hyperbolic equation. This is a very detailed and interesting look at the use of catenary functions in the world of engineering, so make sure to watch this video!

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Related Videos:

Hyperbolic Functions: Catenary: Example 3: Telephone Lines: https://youtu.be/GbDGUYTrHQ0 Hyperbolic Functions: Catenary: Example 2: Graphing Catenaries: https://youtu.be/FlqcdaJn1NU Hyperbolic Functions: Catenary: Example 1: Reverse Proof: https://youtu.be/KK4FoanPHzA Hyperbolic Functions: Catenary: Formula and Proof: https://youtu.be/EYb1p9r1fnM Hyperbolic Functions - tanh(x), sinh(x), cosh(x) - Introduction: http://youtu.be/EmJKuQBEdlc Derivatives of Hyperbolic Trigonometry: cosh(x): http://youtu.be/4AGkxTGxASQ Hyperbolic Trigonometry Identity Proof: cosh^2(x) - sinh^2(x) = 1: http://youtu.be/-UXUqIWRNEA Applications of Integrals: Arc Length Proof: https://youtu.be/2rb4H_rmgxg .

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