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Math Help - Help with parametric equations?

  1. #1
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    Question Help with parametric equations?

    Two particles move in the xy-plane. At time t, the position of particle A is given by x(t)=4t−4 and y(t)=2t−k, and the position of particle B is given by x(t)=3t and y(t)=t^2−2t−1.
    Find k so that the particles are sure to collide.

    My initial thought wast to take the derivatives of the equations, but then the k would just drop out, so that's not right.
    Any suggestions? Thanks!
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    Quote Originally Posted by iheartthemusic29 View Post
    Two particles move in the xy-plane. At time t, the position of particle A is given by x(t)=4t−4 and y(t)=2t−k, and the position of particle B is given by x(t)=3t and y(t)=t^2−2t−1.
    Find k so that the particles are sure to collide.

    My initial thought wast to take the derivatives of the equations, but then the k would just drop out, so that's not right.
    Any suggestions? Thanks!
    If the two particles collide, then surely they have the same x and y values...


    So 4t - 4 = 3t and 2t - k = t^2 - 2t - 1

    From equation 1, t = 4.

    So, when subbed into equation 2, we have

    8 - k = 7.

    What is k?
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