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Math Help - Don't get bit. (Calculus)

  1. #1
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    Don't get bit. (Calculus)

    You are in the center of a circle of radius R. Some angry dog runs exactly along the circumference of the circle and tries its best to bite or eat you. The dog can run 4 times faster than you. Devise a strategy that will let you run away from the circle unharmed. I need this proved numerically. I really just need someone to help me get started.
    Last edited by ineedhelp; December 17th 2007 at 09:58 PM. Reason: My question wasn't being answered.
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  2. #2
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    Lexington, MA (USA)
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    Hello, ineedhelp!

    You are in the center of a circle of radius R.
    Some angry dog runs exactly along the circumference of the circle and tries to bite you.
    The dog can run 4 times faster than you.
    Devise a strategy that will let you run away from the circle unharmed.

    Run toward the point diametrically opposite the dog.
    Code:
                   Dog
                  * o *
              *           *
            *               *
           *                 *
    
          *        You        *
          *         o         *
          *         ↓         *
    
           *                 *
            *               *
              *           *
                  * * *

    He will commit himself by choosing a direction around the circle.
    Let's say he runs clockwise.

    Curve your path so the center of the circle
    . . is always between you and the dog.
    Code:
                  * * *
              *           *
            *               o
           *              /  *
                        /
          *           /       *
          *         *         *
          *       / +        *
                + +
           *                 *
            *               *
              *           *
                  * * *

    You will spiral outward and reach the perimeter
    . . and the dog will still be diametrically opposite.

    Code:
                  * * *
              *           *
            +               *
           *+ \              *
                \
          *  +    \           *
          *         *         *
          *   +     + \       *
                + +     \
           *              \  *
            *               o
              *           *
                  * * *
    I hope your car is close enough for you to sprint to it.

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  3. #3
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    Joined
    Dec 2007
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    How would you solve to show that a person made it out of the circle before the dog got to him/her? I understand that one needs to prove that the dog traveled 4r and you traveled less than that but im not sure how to show it.
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