A Physics Quiz of a different type

[Ether]

Originally Posted by EricH

System 2 (X'Y'): In this case, the system is fixed onto Particle B in the above problem, which is assumed to be moving at -c/2 (from the reference point in System 1's point of view). The relative speed remains the same, as the motion did not change (if viewed from System 1's reference point), so observers on Particle B see Particle A leaving at speed c.

Surprisingly, the above answer is not correct. It is the heart of Einstein's theory of relativity and why it was so profound a discovery that changed the face of physics.

An observer sitting on Particle B (i.e., in reference frame X'Y') will observe Particle A's speed to be

(c/2+c/2)/(1+(c/2)(c/2)/c^2) = 0.8*c

[Aren Siekmeier]

Originally Posted by Ether

Surprisingly, the above answer is not correct. It is the heart of Einstein's theory of relativity and why it was so profound a discovery that changed the face of physics.

An observer sitting on Particle B (i.e., in reference frame X'Y') will observe Particle A's speed to be

(c/2)(c/2)/(1+(c/2)(c/2)/c^2) = 0.8*c

^ninja'd (sort of)

And yeah that. That's the velocity transform: u' = (u+v)/(1+uv/c^2), u is the particle's velocity, v is the velocity of the prime frame relative to the non-prime frame.

[Ether]

Originally Posted by compwiztobe

^ninja'd (sort of)

And yeah that. That's the velocity transform: u' = uv/(1+uv/c^2), u is the particle's velocity, v is the velocity of the prime frame relative to the non-prime frame.

There was a typo in my original post.

The relativistic addition of velocities is (u+v)/(1+u*v/c^2).

[Aren Siekmeier]

Heh, yeah, a little dimensional analysis would tell you that much.... I'm tired.