Need help with Calculus 2 Project.

[Techman07]

Looking for help on a certain project. I have posted the project in pdf format


http://home.ripway.com/2005-5/317800/proj1sum05.pdf

I have already solved the first problem (a), but problem b (finding the angle) doesn't make intuitive sense to me.If you all could be so kind, all ideas are greatly appreciated. Maybe if I understood the question better that would also help.

 

[Corneo]

Well you are given the equation of the curve created by the cable. Thus you can find the tangent line to to curve at $x=\pm b$. Thus you can create a triangle using the tangent line as the hypotenuse, a pole as a vertical leg, and the horizontal line tangent to the minimum of the curve. Try drawing a picture.

 

[Techman07]

number one...

man i don't even think I did number one right now...

 

[whozum]

Maybe you'll see it better if its translated.

A curve with equation y = 2acosh(x/a) intersects the x-axis at x = -b, b. Find the arclength of the curve. All you need to do is integrate arclength for x = -50 to 50.

 

[Techman07]

its the letter a...

I don't mind integrating it, but I just can't figure out what a is...

 

[Pyrrhus]

Have you read the problem? it states a is a positive constant...

Considering real valued functions, this means

$$\{ a \epsilon \Re | a > 0 \}$$

 

[Corneo]

since the distance of the poles from another is 100m, then this means there are poles at $x=\pm 50$. From then you can solve for $a$ since you know that $S = 20$ and you know what $b$ is.

 

[Techman07]

I end up with (a+20 = a cosh(50/a), I know that this in turn is the same as
[a + 20 = a (e^(50/a) + e^-50/a) all over 2). There are too many a's I still don't understand how to simplify, thank you for your help though.