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Homework Help: Lorentz transformation using to find for vx of a missile

  1. Mar 30, 2010 #1
    I have a question which i believe is pretty standard,
    spaceship travelling towards space staion at 0.80c it fires a missile at 0.40c what is the speed of the missle observed by the space station

    I'll tell you where im at;
    I have set 2 inertial frames. A being that of the space station and B being that of the spaceship. I know i am supposed to use Lorentz transformation of;


    I believe the top part is vx-V = (-0.80c)-(0.40c)
    the minus being used due to the fact its travelling towards the space staion.
    Its just the bottom bit i dont understand. Its not as simple as i thought, im not sure what value to assign to c. I thought it was the speed of light at 3*108 but at each example i've looked at they have assigned unique numbers for example....8c and 3c
    ANy help would be great
  2. jcsd
  3. Mar 30, 2010 #2
    You've got things a bit backwards. :)
    It is very important to remember what every symbol stands for in these formulas. The ones you usually commit to memory deal with two inertial reference frames.
    One is the S frame, which is assumed stationary, and the second is the S' frame, which moves with uniform velocity V in the positive X direction relative to the S frame.

    Now that we've gotten our definitions cleared up a bit, let's try and reword the problem.

    Your unprimed frame, S, is the frame of the ship. With relation to the ship, the station is moving with velocity V=-0.8c in the positive x direction. (Note the minus, since all our formulas assume that that the primed frame moves in the positive x direction, where in this case the primed frame actually moves in the negative x direction!)

    The velocity of the missile in the unprimed frame is vx=+0.4c

    Now that we've cleared up what every symbol means, finding the velocity of the missile in the primed frame, vx' should not be difficult since we have the formula:
    [tex]v_x '=\frac{v_x - V}{1-\tfrac{v_x V}{c^2}}[/tex]
    where we have already illuminated what every symbol means.

    Generally, V will stand for the velocity of the primed frame relative to the unprimed frame, in the positive x direction. Unprimed quantities (t, x, vx, etc) will refer to quantities measured in the unprimed frame, while primed quantities (t', x', vx', etc) will refer to quantities measured in the primed frame.

    As for your second question:
    Most of these problems don't require that you know the velocity of light. It's a good number to commit to memory, and an easy one at that, [tex]c=3\cdot 10^8 \tfrac{m}{s}[/tex], but for the most part you'll get velocities as fractions of the speed of light, which means that in all calculations it'll end up canceling out.

    And I'm sure you're mistaken about the examples you've looked at. Do you mean that they assigned numbers such as 0.8c and 0.3c? 8c and 3c are nonsensical velocities to assign to moving objects.
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