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:
f(x) = a cosh(x/a),
where cosh 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 flagpoles are coincident, of course. There is just enough rope to go 30 ft down a 50 ft pole and 20 ft back up to meet the requirement of 20 ft above the ground. The Cosh function is a smokescreen. This puzzle has cost Rural electrical co-ops in the South millions of dollars in lost work from the newbie linemen trying to solve it.......The puzzle for them is where to dig the holes to set the poles for new service. I've seen them nearly go nuts trying.....

Posted by Wayne on 2002-12-25 09:37:09