1. Angular velocity

You are a chicken that cannot fly in the center of a circular chicken coop.

Farmer joe wants to eat you, but he is lazy and will only catch you if you are at some point on the circumference. Also, he moves at a rate 4 times faster than you along the circumference towards the point you are headed for.

If you get to the circumference before the farmer you can trigger an electric fence and he will die. If he gets to the circumference before you he will catch you and eat you.

Is there any point on the circumference that you can get to before farmer joe?

Hint: Angular velocity.

2. Frankly I cannot visualize the problem. If you can, please attach a diagram.

3. So we are in the center.

Whichever direction we move, the farmer moves around the circumference in that direction. Assume he takes the shortest path possible.

You are allowed to change strategies at anytime, in which case the farmer does also. He moves along the circumference towards whichever direction you are headed.

4. "You are a chicken that cannot fly in the center of a circular chicken coop."

Can you explain the above statement?

5. Originally Posted by sa-ri-ga-ma
"You are a chicken that cannot fly in the center of a circular chicken coop."

Can you explain the above statement?
You start at the center of the circle, and you are trying to get to any point on the circumference before the farmer. He moves 4 times faster than you, though.

6. Originally Posted by Anonymous1
You start at the center of the circle, and you are trying to get to any point on the circumference before the farmer. He moves 4 times faster than you, though.
When you start from center and reach the circumference,you are traveling a distance R in time t. During that time the farmer moves through the distance 4R towards you. That means, with respect to the center , he moves through an angle 4 radians. So to escape from him you have move in a direction, which is greater than 4 radians with respect to the position of the farmer.

7. Can you give me an example of what this angle might be?

8. Originally Posted by Anonymous1
Can you give me an example of what this angle might be?