Crossing a Canyon
Date: 10 May 1995 23:44:58 -0400 From: Ryan R. Bullock Subject: Geometry Problem Thank you very much for your help on the soda can a few weeks back. I have another challenging problem that I need some help with. Basically, we're trying to cross a canyon. From a point on one side, a rope stretches across and drops ten feet vertically. That point is 18 feet above the water. It is 75 feet horizontally across the canyon. The rope will be stretched as tight as possible, but when weighted with 200 pounds, stretches 10%. I need to find out if I could cross the canyon without getting wet. I know that at the lowest point, the two segments of rope will have equal angles to horizontal, but I'm not sure where to go next. Any hints would be appreciated. Thanks! Ryan R. Bullock, Master of all computer knowledge (IBM PC's anyway)
Date: 22 May 1995 01:01:00 -0400 From: Dr. Ken Subject: Geometry Problem Hello there! Sorry it's taken us a while to get to your problem. It's a little difficult at the end of our academic year to keep up with everything, what with finals, and moving out of dorm rooms and all. First off, I've got to clarify a couple of points in your problem. I think I might be able to interpret your description of the initial rope position in a couple of different ways: 1) The two ends of the rope are level horizontally, and the rope forms a catenary curve (this is the shape that a rope will form when it spans a canyon. It looks kind of like a parabola, but it's a little different) whose lowest point is 10 feet lower than the anchored ends of the rope, and 18 feet above the surface of the water. 2) One anchored end of the rope is ten feet higher than the other, we're assuming that the rope is stretched so tightly that it resembles a straight line, and the lowest anchored end of the rope is 18 feet above the water. Is one of these right? Basically, to solve to problem, you'll have to find out how long the rope is initially, and then multiply that length by 1.1 to find the weighted length. Then find out at what point along your traverse you'll be at your lowest point, and then see whether there's enough rope there to land you in the drink. 'Course, getting a little wet isn't all that bad, provided it's not too cold! Anyway, if you'd like more help on this problem, please write back and let us know which (if either) model we've got for this traverse. Thanks! -K
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.