A telephone line hangs between two poles 14 m apart....

Question

A telephone line hangs between two poles 14 m apart in the shape of the catenary y = 20cosh(x/20) - 15, where x and y are measured in meters.

 

(a) Find the slope of this curve where it meets the right pole.
(b) Find the angle between the line and the pole.

 

I have no idea where to start.

 

#51, p 263

ANSWER: (a) 0.3572 (b) 70.34°

Answer 1

^{Here's a start:}

 

f(x)= 20 cosh(x/20) - 15

 

find f'(x) = ?? 

Recall: D_xcosh u = -csch²u D_xu

Whoops, wrote down wrong formula for D cosh; should be sinh u D_xu.

 

Can you take it from there, finding f'(7)?  ; 7 is the x-coordinate of the right pole.

 

So, f'(x) = 20 sinh (x/20) (1/20) = sinh (x/20)

and, f'(7) = sinh (7/20) = guess what: 0.357189

 

For the angle between a vertical line (the pole) and a line with a slope from part 1: see http://www.tpub.com/math2/5.htm

 

For a picture see: https://www.desmos.com/calculator/s7ztj3hbie