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Relative motion problem.

  1. Sep 26, 2011 #1
    1. The problem statement, all variables and given/known data
    A plane traveling horizontally to the right at 100 m/s flies past a helicopter that is going straight up at 20 at 20 m/s. From the helicopter's perspective, the plane's direction and speed are:
    a) Right and up, less than 100 m/s.
    b) Right and up, 100 m/s.
    c) Right and up, more than 100m/s.
    d) Right and down, less than 100m/s.
    e) Right and down, 100 m/s.
    f) Right and down, more than 100 m/s.

    2. Relevant equations
    [itex]\vec{v} = \vec{v}' + \vec{V}[/itex]
    [itex]\vec{v}[/itex] = velocity of the object in the helicopter's reference frame.
    [itex]\vec{V}[/itex] = the relative velocity measured between two reference frames
    [itex]\vec{v}'[/itex] = velocity of the plane relative to the helicopter's reference frame.
    3. The attempt at a solution
    Just a conceptual question that I do not have the answer to that appeared at the end of the chapter of my text. If the helicopter's reference frame is reference frame S, then the plane would have a vertical velocity component of -20 m/s and horizontal velocity component of 100 m/s. Using the equation:
    [itex]\vec{v} = \vec{v}' + \vec{V}[/itex]
    [itex]\vec{v} = (100\hat{i} - 20\hat{j}) m/s[/itex]
    [itex]\vec{v} =\sqrt{(100^{2}) - (20^{2})}m/s \approx 102 m/s[/itex]
    Therefore, relative to the helicopter's reference frame, the plane's velocity would be f) right and down, more than 100 m/s. Correct?
     
  2. jcsd
  3. Sep 26, 2011 #2
  4. Sep 26, 2011 #3
    Great. Thank you. :biggrin:
     
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