Einstein velocity addition rule

[ehrenfest]

Car 1 is traveling at 3/4c. Car 2 in behind Car 1 is traveling 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?

 

[Janus]

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.

 

[learningphysics]

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?

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.

 

[Gokul43201]

Car 1 is traveling at 3/4c. Car 2 in behind Car 1 is traveling at 1/2c. Car2 fires a bullet that travels at 1/3 c.

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

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?

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?

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