Calc11_2 HypFuncApp

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

This preview shows pages 1–8. Sign up to view the full content.

Applications of Hyperbolic Functions Greg Kelly, Hanford High School, Richland, Washington

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
Another example of a catenary is the Gateway Arch in St. Louis, Missouri.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Another example of a catenary is the Gateway Arch in St. Louis, Missouri.
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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
boat semi-truck A third application is the tractrix. (pursuit curve) An example of a real-life situation

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern