March 13, 2008

Four Dogs

There are four dogs, each at a corner of a large square.
Each of the dogs begins chasing the dog clockwise from it.
All of the dogs run at the same speed. All continuously
adjust their direction so that they are always heading
straight toward their clockwise neighbor. How long does it
take for the dogs to catch each other? Where does this
happen?

7 comments:

  1. God.VMarch 13, 2008 at 2:33 AM

    gud ques dude..
    in the following manner on walking the dogs make a spiral..which ultimately coincides at the centroid of the given figure..if fact true for all regular figires...for a square the co-inciding occures at its centre...

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  2. UnknownApril 30, 2008 at 5:01 PM

    for a square of edge "a" and if speed of each dog is "v".

    then, all four dogs meet at the centre after a/v time.

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  3. AnonymousJune 7, 2009 at 6:37 PM

    isn't it forever-.-?
    since they are at the corner.. they will be always running straight rite?

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  4. UnknownDecember 29, 2010 at 11:10 PM

    There's only one path in it, they have not mentioned any spiral paths, correct me if i am wrong

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  5. AnonymousOctober 24, 2011 at 9:43 PM

    they meet center of the square

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  6. chaituJanuary 27, 2012 at 3:15 PM

    They run into spiral form, since they are heading directly to thier clock-wise partner. and not to the location they sat.

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  7. UnknownMarch 28, 2012 at 11:14 AM

    they will meet at the center of the square:
    Final displacement :l/sqrt(2)
    velocity component in this direction: v cos 45
    So time taken: l/v

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