Don't get bit. (Calculus)

• Dec 16th 2007, 07:40 PM
ineedhelp
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.
• Dec 16th 2007, 08:48 PM
Soroban
Hello, ineedhelp!

Quote:

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.

• Dec 17th 2007, 12:15 PM
ineedhelp
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.