turtles

turtles

Postby kate » Mon Jun 30, 2008 12:42 pm

N turtles are positioned symmetrically on the edge of a circumference with radius R. In a given moment every turtle goes with speed v towards the one before it, it towards the one before it and so on. After how much time will the turtles meet? The problem isn't hard, but for its entire solution it is better to find the law for movement of every turtle first. And after that find the equation of the trajectory of every turtle.
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Re: turtles

Postby leesajohnson » Wed Jun 01, 2016 5:06 am

It's too confusing.

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Re: turtles

Postby Guest » Wed Jun 01, 2016 7:34 am

Dist. around circle = 2 x Pi x R

Dist. between turtles =( 2 x Pi x R) / N

Assume all move same speed = S and will meet in middle of dist. between them.

Dist. travelled to meet = (Pi x R) / N

Time taken to meet =( Pi x R) / (N x S)
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Re: turtles

Postby Guest » Wed Jun 01, 2016 7:38 am

No....I am wrong....they all move in the same direction towards to one before them..........
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Re: turtles

Postby Guest » Wed Jun 01, 2016 7:43 am

If they all move in the same direction and speed towards the one behind then they will always be the same dist. apart so will never meet. Like the spokes in a wheel.
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Re: turtles

Postby Guest » Wed Jun 01, 2016 4:07 pm

This is a well known problem
http://www.cut-the-knot.org/Curriculum/ ... tles.shtml
Time taken[tex]= \frac{R}{v\sin (180^\circ/N)}[/tex]

Hope this helped,

R. Baber.
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Re: turtles

Postby Guest » Wed Jun 01, 2016 4:08 pm

Sorry the link got broken in the edit
http://www.cut-the-knot.org/Curriculum/ ... tles.shtml

R. Baber.
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