# Thread: Don't get bit. (Calculus)

1. ## 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.

2. 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.

3. 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.