Problem conversion into MATLAB

4. A telephone line hangs between two poles 14 m apart in the shape of a 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, θ between the line and the pole.

Answer 1

[Nishant Gupta]

You can solve your problem using MATLAB as follows:

syms x y
y = 20 * cosh (x/20) -15 ; 

Diffrentiate the equation representing line with respect to x to get slope of it:

f(x) = diff(y,x);

To get slope at the point where line meets pole, put x = 14:

slope = vpa(f(14),4);

Finally, to get the angle between the line and pole at that point use atan fun:

angle  = vpa(90 - rad2deg(atan(slope)),4);

Refer to the following links to get more details about diff, atan and vpa functions:

diff ; atan ; vpa

Answer 2

[Philemon Anaman]

Two poles, one 6 meters tall and one 15 meters tall, are 20 meters apart. A length of wire is attached to the top of each pole and it is also staked to the ground somewhere between the two poles. Where should the wire be staked so that the minimum amount of wire is used?

[Steven Lord]

This sounds like a homework assignment. If it is, show us the code you've written to try to solve the problem and ask a specific question about where you're having difficulty and we may be able to provide some guidance.

If you aren't sure where to start because you're not familiar with how to write MATLAB code, I suggest you start with the free MATLAB Onramp tutorial (https://www.mathworks.com/support/learn-with-matlab-tutorials.html) to quickly learn the essentials of MATLAB.

If you aren't sure where to start because you're not familiar with the mathematics you'll need to solve the problem, I recommend asking your professor and/or teaching assistant for help.