Puzzle #2

[Empirical]

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?

[godeeper]

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?

Are you sure that you have this right. Why should the rope be any distance from the equator?

[Magicman]

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?

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

[Versace 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

[Magicman]

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 = .00000001 Km
.001cm

I would have thought that you were right until I read

http://mathforum.org/mathimages/inde...ound_the_Earth

Magicman

[Versace Targeryan]

I would have thought that you were right until I read

http://mathforum.org/mathimages/inde...ound_the_Earth

Magicman

yess silly sustraction misstake 1st time

[Empirical]

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.