Results 1 to 5 of 5

Math Help - HELP!!! Circle problem

  1. #1
    Junior Member
    Joined
    Sep 2008
    Posts
    61

    HELP!!! Circle problem

    This is the problem:

    Quinn is running aruond the circular track x^2 + y^2 = 10,000, whose radius is 100 meters, at 4 meters per second. Quinn starts at the point (100,0) and runs in the counterclockwise direction. After 30 minutes of running, what are Quinn's coordinates?

    Okay first off, please don't flat out give me the answer cuz I want to do it myself. But I really just don't get how to do it!! So can someone please explain this to me?

    Okay, so one, how do I draw the x^2 + y^2 = 10,000? Is it just a regular circle, the center at the origin, with an 100 meter radius?

    And two, how do I find Quinn's coordinates on the graph? Once I get the circle set up, I'll be able to calculate his distance around the circle I'm sure, but how do I find the exact coordinates?

    THANK YOU SO MUCH, if someone could answer within an hour or two I would be really appreciative, it is pretty urgent
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    Quote Originally Posted by pyrosilver View Post
    This is the problem:

    Quinn is running aruond the circular track x^2 + y^2 = 10,000, whose radius is 100 meters, at 4 meters per second. Quinn starts at the point (100,0) and runs in the counterclockwise direction. After 30 minutes of running, what are Quinn's coordinates?

    Okay first off, please don't flat out give me the answer cuz I want to do it myself. But I really just don't get how to do it!! So can someone please explain this to me?

    Okay, so one, how do I draw the x^2 + y^2 = 10,000? Is it just a regular circle, the center at the origin, with an 100 meter radius?

    And two, how do I find Quinn's coordinates on the graph? Once I get the circle set up, I'll be able to calculate his distance around the circle I'm sure, but how do I find the exact coordinates?

    THANK YOU SO MUCH, if someone could answer within an hour or two I would be really appreciative, it is pretty urgent
    Yes, the circle has its center at (0,0) and its radius is 100 meters.
    Then the initial position of the runner, (100,0), means he is at the point (100,0), . On your drawing , that is at x=100, y=0. Or it is at the x-axis, 100 m from the (0,0).

    Then he ran at 4 m/sec counterclockwise for 30 minutes or (30*60) = 1800 seconds.
    What is the final position Of Quinn then in coordinates form?

    It is easier for me to explain it with computations but you want to do it yourself so....
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2008
    Posts
    61
    Quote Originally Posted by ticbol View Post
    Yes, the circle has its center at (0,0) and its radius is 100 meters.
    Then the initial position of the runner, (100,0), means he is at the point (100,0), . On your drawing , that is at x=100, y=0. Or it is at the x-axis, 100 m from the (0,0).

    Then he ran at 4 m/sec counterclockwise for 30 minutes or (30*60) = 1800 seconds.
    What is the final position Of Quinn then in coordinates form?

    It is easier for me to explain it with computations but you want to do it yourself so....
    Okay, so he goes 7200 meters in 30 minutes?

    So the track is 628.3 meters, right? That means that he goes around 11.459 times. So he goes around 11 times. Then, do I multiply 628.3 and .459? I got 288.390.

    If all that is correct, how do i find the coordinate of it?

    Thanks by the way for replying, I'm really relieved.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    Quote Originally Posted by pyrosilver View Post
    Okay, so he goes 7200 meters in 30 minutes?

    So the track is 628.3 meters, right? That means that he goes around 11.459 times. So he goes around 11 times. Then, do I multiply 628.3 and .459? I got 288.390.

    If all that is correct, how do i find the coordinate of it?

    Thanks by the way for replying, I'm really relieved.
    Okay. My computations say it is 288.5 m past the positive x-axis.
    Meaning, the runner is at 288.5 m counterclockwise from his starting point.

    One way to get that position is by using proportion.
    One revolution, or one circumference, is for 360 degrees.
    So for 2888.5 m arc, that would be for angle theta
    theta / 288.5 = 360 / 200pi
    theta = 360(288.5 / 200pi) = 165.3 degrees.

    That means the runner is in the 2nd quadrant.
    Its y-coordinate is 100*sin(165.3 deg) = 25.38 m.
    Its x-coordinate is 100cos(165.3 deg) = -96.73 m
    Therefore, the runner now is at (-96.73, 25.83) ----answer.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Sep 2008
    Posts
    61
    Quote Originally Posted by ticbol View Post
    Yes, the circle has its center at (0,0) and its radius is 100 meters.
    Then the initial position of the runner, (100,0), means he is at the point (100,0), . On your drawing , that is at x=100, y=0. Or it is at the x-axis, 100 m from the (0,0).

    Then he ran at 4 m/sec counterclockwise for 30 minutes or (30*60) = 1800 seconds.
    What is the final position Of Quinn then in coordinates form?

    It is easier for me to explain it with computations but you want to do it yourself so....
    Quote Originally Posted by ticbol View Post
    Okay. My computations say it is 288.5 m past the positive x-axis.
    Meaning, the runner is at 288.5 m counterclockwise from his starting point.

    One way to get that position is by using proportion.
    One revolution, or one circumference, is for 360 degrees.
    So for 2888.5 m arc, that would be for angle theta
    theta / 288.5 = 360 / 200pi
    theta = 360(288.5 / 200pi) = 165.3 degrees.

    That means the runner is in the 2nd quadrant.
    Its y-coordinate is 100*sin(165.3 deg) = 25.38 m.
    Its x-coordinate is 100cos(165.3 deg) = -96.73 m
    Therefore, the runner now is at (-96.73, 25.83) ----answer.
    Aah, I think i got it now. Thank you SO MUCH for taking the time to help me out!! i appreciate it A LOT!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Circle problem
    Posted in the Advanced Math Topics Forum
    Replies: 3
    Last Post: May 20th 2011, 10:20 AM
  2. Circle Problem
    Posted in the Geometry Forum
    Replies: 2
    Last Post: November 8th 2010, 03:40 PM
  3. circle problem
    Posted in the Geometry Forum
    Replies: 8
    Last Post: April 23rd 2010, 10:13 AM
  4. Circle Problem
    Posted in the Geometry Forum
    Replies: 5
    Last Post: May 12th 2009, 10:27 AM
  5. circle problem
    Posted in the Geometry Forum
    Replies: 4
    Last Post: November 9th 2008, 11:32 AM

Search Tags


/mathhelpforum @mathhelpforum