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Homework Help: Determine the magnitude of and direction of the velocity

  1. Oct 9, 2007 #1
    I have problems on understanding Relativity.So can someone check this one.
    1. The problem statement, all variables and given/known data



    2. Relevant equations
    A spacecraft is launched from the surface of the with velocity of 0.600c at an angle of
    [tex]50^{\circle}[/tex] above the horizontal positive x axis.Another spacecraft is moving past,with a velocity of 0.700c in the negative x direction..Determine the magnitude of and direction of the velocity of the first spacecraft as measured by the pilot of the second spacecraft.


    3. The attempt at a solution
    [tex]v_{1x}=0.6c\times cos50^{\circle}[/tex]
    [tex]v'_x=\frac{v_{1x}+v_2}{1+\frac{v_{1x}v_2}{c^2}}[/tex]
    [tex]v'_y=v_1sin50^{\circle}[/tex]
    [tex]v'=\sqrt{v'_x+v'_y}[/tex]
    [tex]tan\theta'=\frac{v'_y}{v'_x}[/tex]
     
    Last edited by a moderator: Jan 7, 2014
  2. jcsd
  3. Oct 9, 2007 #2

    MathematicalPhysicist

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    Gold Member

    the equation in the y direction is:
    [tex]v_y'=\frac{v_y}{(1+v_xv/c^2)\gamma(v))}[/tex]
    other than this it looks good to me.
     
  4. Oct 9, 2007 #3
    Like this
    [tex]v'_y=\frac{v_1sin50\sqrt{1-v_1^2/c^2}}{(1+v_1^2cos50/c^2)}[/tex]?
     
  5. Oct 9, 2007 #4
    but should be there similar equation for [tex]v_{1x}[/tex] ?
     
  6. Oct 9, 2007 #5

    learningphysics

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    Homework Helper

    I think it's best to use these equations:

    [tex]u_x' = \frac{u_x - v}{1-u_x v/c^2}[/tex]

    [tex]u_y' = \frac{u_y}{\gamma (1-u_x v/c^2)}[/tex]

    v is the velocity of the second ship... ie v = -0.700c, and ux' and uy' are the speeds measured by this second ship...

    just plug in ux, uy, v and gamma and you'll have the answers.
     
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