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Advanced Vector Problem: Ships

  1. Jan 23, 2016 #1
    1. The problem statement, all variables and given/known data
    Three ships A, B, and C move with velocities [itex]\vec{v_{1}} \ \vec{v_{2}} \ \vec{u}[/itex] respectively. The velocities of A and B relative to C are equal in magnitude and perpendicular. Show that [itex]\left | \vec{u} -\frac{1}{2}(\vec{v_{1}} + \vec{v_{2}}) \right |^{2} = \left | \frac{1}{2}(\vec{v_{1}} - \vec{v_{2}}) \right |^{2}[/itex]

    2. Relevant equations
    Algebraic scalar product, vector product(?), magnitude of a vector.

    3. The attempt at a solution
    WIN_20160123_17_54_51_Pro.jpg
     
  2. jcsd
  3. Jan 23, 2016 #2

    PeroK

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    I can't see very well what you've done. Why not start with the condition that the relative velocities are perpendicular? What does that give you?
     
  4. Jan 23, 2016 #3

    SammyS

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    The relative velocities are ##\ \vec{v_1}-\vec{u} \ ## and ##\ \vec{v_2}-\vec{u} \ ##

    NOT ##\ \vec{v_1}+\vec{u} \ ## and ##\ \vec{v_2}+\vec{u} \ ##
     
  5. Jan 23, 2016 #4
    I tried scalar product and equating to zero but as SammyS just noticed the problem seems to be in the initial statement that v1 + u is the relative velocity in the first place. Thank you!
     
  6. Jan 23, 2016 #5
    Thank you very much.
     
  7. Jan 23, 2016 #6

    Mark44

    Staff: Mentor

    Moved to Precalc section, as there is no calculus involved.
     
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