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Topic: North by North-west (Read 1253 times) |
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ThudnBlunder
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North by North-west
« on: Apr 6th, 2003, 1:01pm » |
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If we begin at the equator and keep moving due north-west, where will be end up??
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THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.
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stpalli
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Re: North by North-west
« Reply #1 on: Apr 6th, 2003, 2:03pm » |
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U will reach the north pole
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ThudnBlunder
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Re: North by North-west
« Reply #2 on: Apr 6th, 2003, 2:16pm » |
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But how can you reach the north pole travelling north-west if every line from the north pole leads south? 
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THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.
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aero_guy
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Re: North by North-west
« Reply #3 on: Apr 6th, 2003, 5:54pm » |
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Limits. Theoretically you should never get there, but eventually you will.
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Chronos
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Re: North by North-west
« Reply #4 on: Apr 6th, 2003, 7:39pm » |
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What's more, you'll only travel a finite distance in doing so. However, you will pass around the pole (cross every longitude line) an infinite number of times in the process.
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Icarus
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Re: North by North-west
« Reply #5 on: Apr 6th, 2003, 9:05pm » |
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You'll also get so dizzy, you won't care where you are anymore!
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aero_guy
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Re: North by North-west
« Reply #6 on: Apr 7th, 2003, 12:30am » |
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I figure after the five hundreth revolution or so you will fall down... onto the pole since it should be in easy reach by that point.
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ThudnBlunder
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Re: North by North-west
« Reply #7 on: Apr 7th, 2003, 2:55am » |
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Yes, the route traced out is called a loxodrome, an equiangular spiral on a sphere. And the distance travelled will be sqrt(2)*longitudinal distance of equator from pole.
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| « Last Edit: Apr 7th, 2003, 4:56am by ThudnBlunder » |
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ThudnBlunder
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Re: North by North-west
« Reply #8 on: Apr 7th, 2003, 3:40pm » |
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Quote:| U will reach the north pole |
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And what time will it be when you get there? 
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| « Last Edit: Jan 29th, 2004, 5:41pm by ThudnBlunder » |
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ThudnBlunder
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Re: North by North-west
« Reply #10 on: Apr 7th, 2003, 11:11pm » |
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on Apr 7th, 2003, 8:52pm, SWF wrote:
OK, ignoring the Coriolis force, what time was it in that puzzle?
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| « Last Edit: Jan 29th, 2004, 5:40pm by ThudnBlunder » |
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aero_guy
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Re: North by North-west
« Reply #11 on: Apr 8th, 2003, 9:58am » |
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How long it takes depends on how wide your feet are.
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Chronos
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Re: North by North-west
« Reply #12 on: Apr 9th, 2003, 8:31pm » |
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Since it's a finite distance, and we can reasonably assume a constant speed, the total time should be finite. This is true even if you're a perfect point, and gives an excellent approximation even with wide feet (since your feet are much smaller than the Earth, the last bit you skip by stomping on the pole is much less than the distance you covered coming all the way from the Equator). But even if you can say how long it takes you to get there, you can't say what the local time will be when you arrive.
Related fact, by the way: On a Mercator projection map, this path would be represented by a straight line. This is the value of the Mercator projection, and why it's useful in navigation, not the supposed reason that it inflates Europe at the expense of Africa. Thinking a bit about this property of Mercator should also show you why you can't show the poles on such a map.
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