Calc11_2 HypFuncApp - that can be modeled by a tractrix...

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Applications of Hyperbolic Functions Greg Kelly, Hanford High School, Richland, Washington
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Even though it looks like a parabola, it is not a parabola! A hanging cable makes a shape called a catenary . cosh x y b a a = + (for some constant a ) sinh dy x dx a = Length of curve calculation: 2 1 d c dy dx dx + 2 1 sinh d c x dx a + 2 cosh d c x dx a cosh d c x dx a sinh d c x a a
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Another example of a catenary is the Gateway Arch in St. Louis, Missouri.
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Another example of a catenary is the Gateway Arch in St. Louis, Missouri.
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If air resistance is proportional to the square of velocity: ( 29 ln cosh y A Bt = y is the distance the object falls in t seconds. A and B are constants.
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boat semi-truck A third application is the tractrix. (pursuit curve) An example of a real-life situation
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Unformatted text preview: that can be modeled by a tractrix equation is a semi-truck turning a corner. Another example is a boat attached to a rope being pulled by a person walking along the shore. → boat semi-truck A third application is the tractrix. (pursuit curve) Both of these situations (and others) can be modeled by: 1 2 2 sech x y a a x a- =-- a a → The word tractrix comes from the Latin tractus , which means “to draw, pull or tow”. (Our familiar word “tractor” comes from the same root.) Other examples of a tractrix curve include a heat-seeking missile homing in on a moving airplane, and a dog leaving the front porch and chasing person running on the sidewalk. π...
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