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?
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?
Last edited by Empirical; 03-08-14 at 21:59.
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
Last edited by Versace Targeryan; 03-08-14 at 23:18.
I would have thought that you were right until I read
http://mathforum.org/mathimages/inde...ound_the_Earth
Magicman
Versace Targeryan (03-08-14)
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.
Last edited by Empirical; 05-08-14 at 14:18.
I would imagine that the source of the question is probably
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