Recall that the equation of a hanging cable is
y = a cosh(x/a)
where 2a is the distance between the poles and a is the height of the lowest point of the cable. Now, that has a minimum height of y=a, which we cannot guarantee. So, let's include a scale factor of k, giving us a curve of
y=k*cosh(x/a)
where y(a)=50 and the arc length from 0 to a is 40. That means you have to solve
∫[0..a] √(1+(k/a sinh(x/a))^2) dx = 40
k*cosh(a)=50
See what you can do with that.
A cable of 80m is hanging from the top of two poles that are both 50m from the ground.
What is the distance between the two poles, to one d.p., if the center of the cable is:
a) 20m above the ground
b) 10m above the ground
Answers to the questions are:
a) 45.54m
b) (somewhat a trick answer) 0m
Any help is appreciated, thanks!
1 answer
2 answers