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| Thread ID: 127344 | 2012-10-18 06:26:00 | math problem for my daughter | mohadino (14141) | PC World Chat |
| Post ID | Timestamp | Content | User | ||
| 1307459 | 2012-10-18 06:54:00 | The key words to this problem are 'great circle distances between cities' This should start you off on the right track . Correct, but Mohadino, you still need the latitude and longitude of origin and destination to start . What is your daughter studying that she is asked questions like that? That used to be the stuff of senior commercial pilot license exams . |
WalOne (4202) | ||
| 1307460 | 2012-10-18 07:44:00 | Hmm, I'd be keen to see the exact wording of the challenge. Is it actually meant to be travelling distance? - which would be a chord (an arc) across the surface of the globe, or is it referring to a direct path, being subterranean in a straight line between the cities? It also, incorrectly assumes the world is a perfect sphere, which it isn't, being wider about the equator thanks to the influence of its spin. It may be that getting the correct interpretation (over ground / under ground) is the real challenge to the question, rather than the number submitted as an answer. |
Paul.Cov (425) | ||
| 1307461 | 2012-10-18 07:53:00 | It would have to be a Great Circle route. Anything else would be far too complex, especially any subterranean route! And would serve no useful navigational purpose whatsoever. |
WalOne (4202) | ||
| 1307462 | 2012-10-18 08:03:00 | Going way back, the sort of question we would have been given, probably 1st year at uni maths for physics would have been along the lines: 'Assuming the earth can be represented by a sphere, derive from first principles an expression for the great circle distance between two points on the surface of the sphere in terms of the latitudes and longitudes of the points and the radius r of the sphere' Then there would have been a numerical calculation using that expression. Log tables may be used :) Wiki gives the formulae, but not the derivations en.wikipedia.org Edit: in principle it is an easy exercise, from the latitudes and longitudes calculate the angle θ subtended in a plane passing through the points and the centre of the sphere, the great circle distance is then rθ |
Terry Porritt (14) | ||
| 1307463 | 2012-10-18 08:35:00 | Ring the travel agent and ask for the price between the points mentioned. Ask them what the average seat/mile cost cost is for the trip, and simple arithmetic gives an answer. Note, it is important that your daughter understands that a landline POT is more economic for the research phase, and still has adequate accuracy in spite of being only analogue. ;) | R2x1 (4628) | ||
| 1307464 | 2012-10-18 08:41:00 | It's a tough question, I'd use spherical trig, you have your lat/longitudal Pts so it's just a matter of substitution. Luckily with the internet I'm guessing some simple trig is in hand, since we can use numbers pre worked out to find the distance along a flat plane rather that differentiating the equation and pulling out the log tables (or rather the log function on your graphic calculator today :D I'm doing poorly in L3 Calc at the moment, doubt I'm gonna be much use :rolleyes: |
The Error Guy (14052) | ||
| 1307465 | 2012-10-18 11:30:00 | Are you sure it's not a trick question based on the "Travelling salesman problem" ? | Agent_24 (57) | ||
| 1307466 | 2012-10-18 19:41:00 | google maps should answer that question | beama (111) | ||
| 1307467 | 2012-10-18 20:41:00 | The way I see it the first problem is the question. :D Whereabouts in these City’s are we going? Get the exact Latitudes & Longitudes sorted and the rest is relatively easy. For those that don’t understand, if I’m going by Ship I don’t want the coordinates for the Airport and vice versa. ;) You could always ask the teacher, "How long is a piece of string?" ;) |
B.M. (505) | ||
| 1307468 | 2012-10-19 05:52:00 | A piece of string stretched across a globe between cities, then compared against the scale on the globe is another easy aproximation. Must be aware that a 2D map misrepresents the distances badly when changing to different longitudes. |
Paul.Cov (425) | ||
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