Question

Answer in MATLAB format. 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

clear all
clc
%% distance between poles
dist = 14; % in meters
x = 0:0.1:14; % simulation iteraion of x
% Calculate the shape of y
y = 20*cosh(x./20) - 15;
% locus of y with respect to x
figure(1)
plot(x,y)
grid
title('locus of line between two poles')
xlabel('distance between poles (in meters)')
ylabel('locus of line')
% Deteremine slope of curve
slopeY = diff(y)/0.1;
% plot the slope trajectory
figure(2)
plot(x(2:end),slopeY)
grid
title('slope of the line')
xlabel('distance between poles (in meters)')
ylabel('slope of line')
% find angle
theta = atand(slopeY);
% plot the angle
figure(3)
plot(x(2:end),theta)
grid
title('angle of the line')
xlabel('distance between poles (meters)')
ylabel('angle of line (degree)')

the locus of the line is shown below

the slope of the line is shown below

the angle of the line is shown below

the maximum angle between the line and the rightmost pole is 37.02 degree.