Results 1 to 10 of 10

Math Help - Angular velocity

  1. #1
    Super Member Anonymous1's Avatar
    Joined
    Nov 2009
    From
    Big Red, NY
    Posts
    517
    Thanks
    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.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jun 2009
    Posts
    806
    Thanks
    4
    Frankly I cannot visualize the problem. If you can, please attach a diagram.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member Anonymous1's Avatar
    Joined
    Nov 2009
    From
    Big Red, NY
    Posts
    517
    Thanks
    1
    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.
    Attached Thumbnails Attached Thumbnails Angular velocity-screen-shot-2010-04-13-9.36.39-am.png  
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Jun 2009
    Posts
    806
    Thanks
    4
    "You are a chicken that cannot fly in the center of a circular chicken coop."

    Can you explain the above statement?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member Anonymous1's Avatar
    Joined
    Nov 2009
    From
    Big Red, NY
    Posts
    517
    Thanks
    1
    Quote Originally Posted by sa-ri-ga-ma View Post
    "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.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member
    Joined
    Jun 2009
    Posts
    806
    Thanks
    4
    Quote Originally Posted by Anonymous1 View Post
    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.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member Anonymous1's Avatar
    Joined
    Nov 2009
    From
    Big Red, NY
    Posts
    517
    Thanks
    1
    Can you give me an example of what this angle might be?

    Thanks for your help.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Super Member
    Joined
    Jun 2009
    Posts
    806
    Thanks
    4
    Quote Originally Posted by Anonymous1 View Post
    Can you give me an example of what this angle might be?

    Thanks for your help.
    To answer the above question, one more clarification is needed. Whether the farmer always moves with constant speed equal to 4 times the speed of the chicken?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Super Member Anonymous1's Avatar
    Joined
    Nov 2009
    From
    Big Red, NY
    Posts
    517
    Thanks
    1
    yes.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Super Member
    Joined
    Jun 2009
    Posts
    806
    Thanks
    4
    Quote Originally Posted by Anonymous1 View Post
    yes.
    If the chicken starts from the center and moves in any direction, other than towards the farmer, farmer crosses point on the circumference in that direction before chicken reaches that point.
    If the chicken starts from a point on the circumference, just in time when the farmer reaches that point, he can catch the chicken if 4 times the length of he chord is equal to distance along the circumference to the other end of the chord.
    In any case, it appears that the farmer must starve for the time being.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Angular Velocity
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: January 16th 2011, 07:25 PM
  2. Angular Velocity
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: May 25th 2010, 04:03 PM
  3. angular velocity
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: November 28th 2009, 08:01 AM
  4. angular velocity
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: November 13th 2009, 04:45 PM
  5. angular velocity
    Posted in the Math Topics Forum
    Replies: 4
    Last Post: November 9th 2008, 11:37 AM

Search Tags


/mathhelpforum @mathhelpforum