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Math Help - Circle Angle, Time: xy coordinates

  1. #1
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    Circle Angle, Time: xy coordinates

    A ferris wheel is rotating at the constant angular speed of 3 RPM counterclockwise. The platform of this ferris wheel is a circular disc of radius 24 feet. You jump onto the ferris wheel at the location pictured below.
    Circle Angle, Time: xy coordinates-uw-precalc-17.5.png
    If θ = 34o, then what are your xy coordinates after 4 minutes?
    If θ = 20o, then what are your xy coordinates after 45 minutes?

    So for both of these, which are similar problems, but different degree and timing, I'll start with the first one
    First I know that the time is 4 minutes
    I also know sin (34o) = 0.559192904
    Then θ = wt = (3 rev/min)(4 minutes)(2pi/1rev) = 75.39822369 radians

    Though, I'm not sure if I'm doing it right, since I kind of got lost, but I know the radius is 24
    Then after I get the right degrees, then I would use rcosθ to find x, and rsinθ to find y

    Can anyone help me out here? Thanks





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  2. #2
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    Re: Circle Angle, Time: xy coordinates

    Since you're travelling around the circle at 3 RPM, then after a full minute you have gone around 3 times, but are now back at your starting location. This is true for any number of minutes. So after 4 minutes you are again at your starting location and the same with 45 minutes. At that point you just calculate x and y as you've stated.
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  3. #3
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    Re: Circle Angle, Time: xy coordinates

    I did?
    For the first one, the answer is: (-5.92564, 21.14892)
    And the second one is: (19.07064, -10.89497)

    I'm getting different numbers.
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  4. #4
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    Re: Circle Angle, Time: xy coordinates

    I just used (24 cos 34 \degree , 24 sin 34 \degree ) \approx (19.9, 13.4) and similar for the next
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  5. #5
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    Re: Circle Angle, Time: xy coordinates

    Quote Originally Posted by cshanholtzer View Post
    I just used (24 cos 34 \degree , 24 sin 34 \degree ) \approx (19.9, 13.4) and similar for the next
    The x seems similar, but the y are kind of completely different, one is negative and is 10, the other is positive and is 13
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  6. #6
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    Re: Circle Angle, Time: xy coordinates

    For the values of \theta given you are in the first quadrant so should expect a positive value for both x and y.
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  7. #7
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    Re: Circle Angle, Time: xy coordinates

    Quote Originally Posted by cshanholtzer View Post
    For the values of \theta given you are in the first quadrant so should expect a positive value for both x and y.
    Oh wow, I feel stupid. I posted the wrong answers, anyway I made it hard on myself.
    It was just basically 24cos(34) and 24sin(34)...
    And for the 2nd one is 24(cos20) and 24sin(20)
    Well thanks for your help!
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