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Parametric equations for trajectory

  1. Nov 14, 2009 #1
    1. The problem statement, all variables and given/known data
    A jet takes off from (1, 1, 0) at time t = 0 and moves with constant speed v = (−5, 0, 1).
    In a flight simulator, the trajectory of the jet is displayed in the yz-plane as it would appear to an observer at the point (1, 0, 0). Find the formula (in the form y = y(t), z = z(t)) for the trajectory on the screen.

    2. Relevant equations

    3. The attempt at a solution
    y(t) = 1
    z(t) = t
    Is that right?
  2. jcsd
  3. Nov 15, 2009 #2


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    Science Advisor

    That would be the "parallel projection" onto the yz-plane, not "it would appear to an observer at the point (1, 0, 0)". The position of the jet, in 3 dimensions, is (1- 5t, 1, t). A straight line from (1, 0, 0) through that, in parameter s, would be (1- 5st, 1+ s, ts). That passes through the "yz-plane" (x= 0) when 1- 5st= 0 or s= 1/5t: (0, 1+1/5t, 1/5).
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