
Geometry Geometry Math Forum 
 LinkBack  Thread Tools  Display Modes 
May 9th, 2017, 11:25 PM  #1 
Newbie Joined: May 2017 From: Israel Posts: 1 Thanks: 0  Around the earth in the equator we attach a rope
Around the earth in the equator we attach a rope (we treat the earth as a geometric ball). We add to the scope of the rope 1 meter. The length of the rope that been created is now equals to the scope of the earth + 1 meter. At some point, we pull the rope out. The rope attached the earth along the arc ABC when AM and AC work as tangents The question: is it possible that point M is high enough above the earth that an elephant can pass threw it? In other words, we need to find the altitude M above the earth. Last edited by skipjack; May 10th, 2017 at 12:04 AM. 
May 10th, 2017, 12:43 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 17,919 Thanks: 1383  Rope.PNG Ignoring the earth's curvature, consider a rightangled triangle with hypotenuse AM = 10 m, then X = √(10²  9.5²) m = 3.1225 m approximately, which would allow an elephant to pass. Try using AM = 100 m instead. 
May 11th, 2017, 07:31 PM  #3 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233 
$C_E = 2 \pi r_E $ $C_E + 1m = 2 \pi r_f$ Now solve for $r_f$ $2 \pi r_E + 1m = 2 \pi r_f$ $ \frac{2 \pi r_E + 1m }{2 \pi } = r_f$ Googling the Earths radius in meters and substituting ... $ \frac {2 \pi (6,371,000m) + 1m }{2 \pi } = r_f$ $6,371,000.16m = r_f$ So the height of the rope above the Earth is 16 centimeters. 
May 12th, 2017, 08:38 AM  #4  
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,049 Thanks: 680 Math Focus: Physics, mathematical modelling, numerical and computational solutions  Quote:
 
May 12th, 2017, 10:56 AM  #5  
Member Joined: Feb 2015 From: Southwest Posts: 96 Thanks: 24  Quote:
 
May 12th, 2017, 11:15 PM  #6 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233 
I don't think I made a mistake in the algebra but I may have misinterpreted the question. It's still pretty amazing to me that adding 1 meter to the circumference of the Earth increases the Earth's radius by a comparativly whopping 16 cm , which is actually $ \frac{100 cm}{2 \pi} $ Counterintuitive until you do the math 
May 15th, 2017, 01:33 AM  #7  
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,049 Thanks: 680 Math Focus: Physics, mathematical modelling, numerical and computational solutions  Quote:
 
May 15th, 2017, 01:38 AM  #8 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233 
Well , when you explain it that way it makes sense 

Tags 
attach, earth, equator, rope 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Lateral and vertical pull (weight) of a hanging rope  SerenityNetworks  PreCalculus  0  September 4th, 2014 03:47 AM 
Tension On BridgeRope Problem  geryuu  Calculus  0  December 14th, 2013 02:59 PM 
How to attach an image  Albert.Teng  New Users  2  April 16th, 2012 07:29 PM 
rope  rkey530  Algebra  1  February 8th, 2009 08:24 AM 
Attach a pdf file????  bigli  New Users  1  July 26th, 2007 05:07 AM 