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Einstein velocity addition rule

  1. Aug 25, 2007 #1
    Car 1 is travelling at 3/4c. Car 2 in behind Car 1 is travelling at 1/2c. Car2 fires a bullet that travels at 1/3 c.

    OK. In order to determine whether the bullet reaches Car 1 or not we need to use Einsteins velocity addition rule and determine whether the relative velocity of the bullet with respect to Car 1 is positive or negative, correct?

    Is it safe in special relativity to say that the velocity of Car 2 with respect to Car 1 is 1/2c - 3/4c? Or do I need to do another velocity addition rule to calculate that?
  2. jcsd
  3. Aug 25, 2007 #2


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    Actually you can just use the velocity addition rule to add the bullet's velocity to car 2's velocity and see if the answer exceeds the velocity of car 1.
  4. Aug 25, 2007 #3


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    You don't need to calculate this velocity, but this velocity is not 1/2c-3/4c. You would use relativistic velocity addition or transformation of velocity to calculate this.

    Although I'm able to see what the question is asking, it's a little ambiguous because you haven't given what 3/4c, 1/2c and 1/3c are relative to... I assumed that the 3/4c and 1/2c are relative to some stationary observer, and the 1/3c is in the backwards direction relative to car 2.
    Last edited: Aug 25, 2007
  5. Aug 25, 2007 #4


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    I imagine this bullet travels at c/3 relative to car 2, though this isn't explicitly stated.


    No, you can not simply subtract the numbers; you must apply the relativistic formula.
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