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Pariah

The Academics Thread

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The list of lengths of various countries' old miles makes for interesting reading, there being a spread of about a factor of three among various European miles.  I seem to recall that the Swedish mile was just about the longest, while the English (and old Roman) were towards the short end.

 

Nautical miles are something entirely different; those are one minute of arc (angle, not linear distance) along a great circle on or above (for aircraft) the surface of Earth.  Going from nautical miles to kilometers requires knowing how large the Earth is and (for precision) how its shape differs from a sphere.

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Question from today's quiz:

 

Bob and Doug are driving a sled through the frozen wastelands of the great white North. Bob drives the sled 4.95 km at a heading of 125°. Doug then takes over the driving and drives 7.17 km at a heading of 11°.  After Doug’s turn, how far are Bob and Doug from where they started, and in which direction?

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Are we permitted to assume that neither leg crossed the North Pole?

 

More precisely: is this assuming a Euclidean coordinate system on a flat plane, or are effects due to being near the coordinate singularity at the North Pole possibly important?

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20 hours ago, Cancer said:

Are we permitted to assume that neither leg crossed the North Pole?

 

More precisely: is this assuming a Euclidean coordinate system on a flat plane, or are effects due to being near the coordinate singularity at the North Pole possibly important?

 

We assume that the ground is perfectly flat, that the North Pole is infinitely far away, and that the sled travels in the absence of  ground friction and air resistance, like any sensible first-year high school physics class.

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5 minutes ago, Pariah said:

 

We assume that the ground is perfectly flat, that the North Pole is infinitely far away, and that the sled travels in the absence of  ground friction and air resistance, like any sensible first-year high school physics class.

 

I didn’t know you were a flat earther. :D

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1 minute ago, Old Man said:

I didn’t know you were a flat earther. :D

 

Of course the Earth is flat...if you look at a small enough piece of it. You just have to know your limits.

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1 hour ago, Pariah said:

 

We assume that the ground is perfectly flat, that the North Pole is infinitely far away, and that the sled travels in the absence of  ground friction and air resistance, like any sensible first-year high school physics class.

 

For extra credit, do the geometry problem on the sphere, where the distance from the pole to any point in the travel might be comparable to or less than a one-leg travel distance.  Hint: you may need to know the radius of Earth to finish the problem.

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Now you're asking about climate change, circumarctic ecology, and the health of apex predators.  Worthy questions, but probably those could wait a couple of weeks into the term.

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If Bob & Doug are travelling close to the speed of light then in the first leg of their trip they would be warping both time and space thus the 4.95 km is warped. The second leg of their journey doesn’t matter as Bob & Doug are energy. ;) :D 

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