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Topic: Marching Army (II) (Read 490 times) |
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ThudnBlunder
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Marching Army (II)
« on: May 6th, 2003, 9:48pm » |
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B----C----E
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A----D----F
A body of soldiers form a square ABCD whose side is of length 50 metres. In one unit of time, they march forward 50 metres in formation to take up the position DCEF. The army's mascot, a small dog, is standing next to its handler at location A. When the soldiers start marching, the dog begins to run around the moving body in a clockwise direction, keeping as close to it as possible. When one unit of time has elapsed, the dog has made one complete circuit and has got back to its handler, who is now at location D. (We can assume the dog runs at a constant speed and does not delay when turning the corners.)
How far does the dog travel?
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| « Last Edit: May 6th, 2003, 9:51pm by ThudnBlunder » |
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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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Kozo Morimoto
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Re: Marching Army (II)
« Reply #1 on: May 7th, 2003, 12:51am » |
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Instead of writing an essay on how I got the answer and embarassing myself, I get 200.199008. Am I close?
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towr
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Re: Marching Army (II)
« Reply #2 on: May 7th, 2003, 1:06am » |
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let the army move with speed a, the dog with speed d
the dog does one side with speed 50/(d-a), one with 50/(d+a), and two with 50/sqrt(d^2 - a^2)
adding them all gives the same time the army is marching.
50/(d-a) + 50/(d+a) + 2 * 50/sqrt(d^2 - a^2) = t
50/a = t
let's choose a=50 meters per time unit and solve for d
1/(d-50) + 1/(d+50) + 2 * 1/sqrt(d^2 - 50^2) = 1/50
100 * sqrt(d^2 - 2500) + 100·d = d^2 - 2500
10000·(d^2 - 2500) = (d^2 - 100·d - 2500)^2
and numerically I get d = 209.0562722 as the probable answer (the other three solutions are unfit)
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ThudnBlunder
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Re: Marching Army (II)
« Reply #3 on: May 7th, 2003, 2:14am » |
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Quote:Instead of writing an essay on how I got the answer and embarassing myself, I get 200.199008. Am I close?
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Close, but no cigar. What equation did you get?
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| « Last Edit: May 7th, 2003, 2:19am by ThudnBlunder » |
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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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Kozo Morimoto
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Re: Marching Army (II)
« Reply #4 on: May 7th, 2003, 4:36am » |
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I knew I had it wrong the first time. After a rethink and mucking around in Mathematica I get same as towr (with a minor rounding difference)
Instead of d and a for speed I had a for army speed and ad for dog speed expressed relative to army speed and got a multiplier of 4.181138 for d, so D=4.181138 * 50
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| « Last Edit: May 7th, 2003, 4:42am by Kozo Morimoto » |
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