The circumference of the earth at the equator is 40,000 Km.
Imagine a rope this length around the equator. Now add just 2 metres to the rope.
How far away from the equator will the rope be?
Puzzle #2
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03-08-14, 21:58EmpiricalPuzzle #2
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03-08-14, 23:00godeeperQuote:
Originally Posted by Empirical
Are you sure that you have this right. Why should the rope be any distance from the equator? -
03-08-14, 23:11MagicmanI would imagine that the source of the question is probablyQuote:
Originally Posted by Empirical
http://mathforum.org/mathimages/inde...ound_the_Earth
in which case the distance the rope would hover is approx one foot around the circumference of the Earth which is the answer to the question as posed.
Magicman -
03-08-14, 23:13Versace Targeryan
if it was a ring and not a roope
R1 = 40000/2 pi = 6366.19772368 Km
R2 = 40000.002/2 pi = 6366.19804199 Km
R2 - R1 = .0.00031831 Km -
03-08-14, 23:17MagicmanI would have thought that you were right until I readQuote:
Originally Posted by Versace Targeryan
http://mathforum.org/mathimages/inde...ound_the_Earth
Magicman -
03-08-14, 23:19Versace Targeryanyess silly sustraction misstake 1st timeQuote:
Originally Posted by Magicman
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05-08-14, 14:16Empirical
This is another puzzle where the intuitive answer—a few millimetres, say—is wrong. We are confused by the vast size of the earth, and the small extension of the rope.
Let, C = circumference of earth (or any sphere), where R is the radius.
from Euclid, C = 2πR
add 2 metres (2m)
(C +2m) = 2π(R + x) where x is the distance between the sphere and the rope
substitute C = 2πR, and expand
2πR + 2m = 2πR + 2πx
so, 2m = 2πx
so, x = 2m/2π = m/π = m/3.14 (approx), = .318m , or 31.8 cms
Interestingly, the size of the Earth or sphere doesn't matter, a rope 2 metres longer than the circumference will always be 31.8 cms from the surface.