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Math Help - Motion in the xy-plane -- ahhhh

  1. #1
    oxx
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    Motion in the xy-plane -- ahhhh

    Hey, I just found this forum and I could use some help

    The directions read: r(t) is the position of a particle in the xy-plane at time t. Fomd am equation in x and y whose graph is the path of the particle.

    the original problem: r(t) = (cos2t)i + (3sin2t)j

    so far, I have:

    x = cos2t
    y = 3sin2t

    Now I know i have to set they equal to each other, but I can't seem to figure out how to solve one of them for t. Any help would be much appreciated!

    Thanks!
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by oxx View Post
    Hey, I just found this forum and I could use some help

    The directions read: r(t) is the position of a particle in the xy-plane at time t. Fomd am equation in x and y whose graph is the path of the particle.

    the original problem: r(t) = (cos2t)i + (3sin2t)j

    so far, I have:

    x = cos2t
    y = 3sin2t

    Now I know i have to set they equal to each other, but I can't seem to figure out how to solve one of them for t. Any help would be much appreciated!

    Thanks!
    x = cos2t
    y = 3sin2t\implies\frac{y}{3}=sin2t

    Eliminate t from these 2 equations using cos^22t+sin^22t=1.
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  3. #3
    oxx
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    Thanks, I think that helped a lot.

    I got an answer of y = 3 (1 +x^2)^(1/2)

    does that look right?
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  4. #4
    MHF Contributor Calculus26's Avatar
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    Actually it is x^2 + (y^2)/9 = 1

    which is an ellipse

    The formula you gave is only the upper half.

    The parametric eqns generate the entire ellipse as t varies from 0 to pi
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