A telephone line hangs between two poles 20 meters apart in the shape of a catenary y=25cosh(x/10)-15, where the center of the line is at x=0 and the poles are at x=±10. Assume both x and y are in meters. Find the slope of this curve where it meets the right telephone pole.

Question

kittiwitti1 · Answer

catenary:$$y=25\cosh{\frac{x}{10}}-15$$

soggylearnsandhelps · Answer

a) This problem is set up nicely for the derivative 

The derivative of cosh is sinh. And, by the chain rule the 1/25 inside cancels with the 25 outside, so you get 

dy/dx = sinh(x/25 - 15) plug in 20 and get the slope 

b) If you have the slope from above, recall that slope is just rise over run, y/x! That is just that cotangent of the angle you are looking for. 
Call the slope from part a 'a'

soggylearnsandhelps · Answer

Y intercepts: (0,10)

kittiwitti1 · Answer

So... deriving for tangential slope?

soggylearnsandhelps · Answer

Yes, I believe so,

soggylearnsandhelps · Answer

NP! I wasn't sure if i could help but looked like i could!

kittiwitti1 · Answer

Oh, that makes it much easier!
Thank you for clarifying. :-)

kittiwitti1 · Answer

... ?? lag