perplexus.info :: Calculus : Enough Rope to Shoot Yourself in the Foot

Enough Rope to Shoot Yourself in the Foot (Posted on 2002-12-22)

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?

Submitted by friedlinguini

Rating: 3.0000 (6 votes)

Solution: (Hide)

0 feet. They are right next to each other. The rope is simply doubled up on itself, and despite the category, no calculus is actually needed.
(It takes 30 feet of rope to reach from the 50 foot top of pole 1 to the low point of 20 feet. The remaining 20 feet are needed to go back up to the 40 foot elevation of pole 2.)

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
good fake	rixar	2004-06-05 22:26:37
re: solution	np_rt	2002-12-25 19:02:05
solution	Wayne	2002-12-25 09:37:09
Got one!	TomM	2002-12-25 02:59:07
Solution	np_rt	2002-12-24 23:41:13
a try	ananth	2002-12-24 01:32:58
re(2): Hrmph...	TomM	2002-12-24 00:16:29
DOH!	levik	2002-12-23 07:02:38
re: Hrmph...	levik	2002-12-23 06:58:27
Hrmph...	levik	2002-12-23 06:56:07
solution	Cory Taylor	2002-12-23 04:00:33
No Subject	Cory Taylor	2002-12-23 03:58:51

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