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Parametric motion in 3-space

  1. Oct 20, 2012 #1
    1. The problem statement, all variables and given/known data

    The base of a 20-meter tower is at the origin; the base of a 20-meter tree is at (0,20,0). The ground is flat & the z-axis points upward. The following parametric equations describe the motion of six projectiles each launched at time t = 0 in seconds. (i refers to x-axis, j refers to y-axis, & k refers to z-axis)

    1) r(t) = (20 + t^2)k
    2) r(t) = (2(t^2))j + (2(t^2))k
    3) r(t) = 20i + 20j + (2-t^2)k
    4) r(t) = 2tj + (20-t^2)k
    5) r(t) = (20-2t)i + 2tj + (20-t)k
    6) r(t) = ti + tj + tk

    A) Which projectile hits the top of the tree?
    B) Which projectile is NOT launched from somewhere on the tower & hits the tree?

    2. The attempt at a solution

    At t = 0,
    1) r = <0, 0, 20>
    2) r = <0, 0, 0>
    3) r = <20, 20, 20>
    4) r = <0, 0, 20>
    5) r = <20, 0, 20>
    6) r = <0, 0, 0>

    These are just guesses
    A) II, B) VI
     
  2. jcsd
  3. Oct 20, 2012 #2

    SammyS

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    Why is A correct? At what value of t does the projectile impact the top of the tree?

    For B: What are the coordinates of the tower?
     
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