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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


God.V said...

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...

saurabh said...

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.

Anonymous said...

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

Mustafa said...

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

Anonymous said...

they meet center of the square

chaitu said...

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

Unknown said...

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