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Thread: Puzzle #2

  1. #1
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    Default Puzzle #2

    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 22:59.

  2. #2

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    Quote Originally Posted by Empirical View Post
    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?

  3. #3
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    Quote Originally Posted by Empirical View Post
    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
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    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; 04-08-14 at 00:18.

  5. #5
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    Quote Originally Posted by Versace Targeryan View Post
    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
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  6. The Following User Says Thank You to Magicman For This Useful Post:

    Versace Targeryan (04-08-14)

  7. #6
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    Quote Originally Posted by Magicman View Post
    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

  8. #7
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    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 15:18.

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