Enough of Calculus
A rope with its two ends held in place forms a curve called a catenary (assuming that the stiffness of the rope is negligible). A catenary takes the shape of the function:
where is the hyperbolic cosine function.
If a 50 foot rope hangs by its ends from two flagpoles, one 50 feet tall and one 40 feet tall, and at its lowest point is 20 feet above the ground, how far apart are the flagpoles?
The answer is 0.
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1 solution
Ans : 0 . They are right next to each other. The rope is simply doubled up on itself. No calculus required!
(It takes 3 0 feet of rope to reach from the 5 0 foot top of pole 1 to the low point of 2 0 feet. The remaining 2 0 feet are needed to go back up to the 4 0 foot elevation of pole 2.)