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u_think_u_succeed
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'Bug'gy Puzzle
« on: Jul 31st, 2007, 7:22am » |
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There are 4 bugs placed at the corners of a square of side 's'. Each bug, when moving. moves at a speed of 'b'.
Now, all four bugs start moving towards each other, and maintain their 'moving toward each other act' throughout, until they meet.
1. Where do they meet.
2. What is the distance covered by each bug.
3. Time when the bugs meet.
Now, try the above for
a) Three bugs on an equilateral triangle.
b) Five bugs on a regular pentagon.
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towr
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Re: 'Bug'gy Puzzle
« Reply #1 on: Jul 31st, 2007, 7:34am » |
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I think it makes a bit of a difference how they move towards each other. You probably want something like "each bug moves to the one that started on the next corner clockwise" That way you get spiraling paths
If the bugs (in the square, or another even-sided) case moved to the one in the opposite corner it wouldn't be very interesting.
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u_think_u_succeed
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Re: 'Bug'gy Puzzle
« Reply #2 on: Jul 31st, 2007, 7:39am » |
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Quote:| You probably want something like "each bug moves to the one that started on the next corner clockwise" |
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Yup, sorry for not specifying it.
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jollytall
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Re: 'Bug'gy Puzzle
« Reply #3 on: Jul 31st, 2007, 11:12pm » |
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They move exactly the same way as four missiles move after the first period of their flight.
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nitinvashist
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Re: 'Bug'gy Puzzle
« Reply #4 on: Sep 27th, 2007, 6:56am » |
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What about bugs at end of equilateral triangle and polygon?
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towr
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Re: 'Bug'gy Puzzle
« Reply #5 on: Sep 27th, 2007, 7:14am » |
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There shouldn't be much of a qualitative difference in those cases. They'd still spiral inwards
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nitinvashist
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Re: 'Bug'gy Puzzle
« Reply #6 on: Sep 27th, 2007, 7:58am » |
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Surely, but it should be more spiral than say a square, and consequently the distance travelled should be more (I think).
I am looking for a general solution for n sided polygon of even/odd sides and the distance travelled before the bugs meet.
Is there a way to calculate the distance travelled using the relative motion of bugs?
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towr
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Re: 'Bug'gy Puzzle
« Reply #7 on: Sep 27th, 2007, 8:47am » |
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on Sep 27th, 2007, 7:58am, nitinvashist wrote:| Surely, but it should be more spiral than say a square, and consequently the distance travelled should be more (I think). |
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That makes sense, as n goes to infinity, they should end up going in a circle.
Quote:| I am looking for a general solution for n sided polygon of even/odd sides and the distance travelled before the bugs meet. |
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A general solution is mentioned in the first post of the thread Jollytall linked to (i.e. here).
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