- #1

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- Homework Statement
- Two particles are created in a high-energy accelerator and move off in opposite directions. The speed of one particle, as measured in the laboratory, is 0.65c, and the speed of each particle relative to the other is 0.95c. What is the speed of the second particle, as measured in the laboratory?

- Relevant Equations
- ##v_x' = \frac{v_x - u}{1 - uv_x/c^2}## (1)

##v_x = \frac{v_x' + u}{1 + uv_x'/c^2}## (2)

Heres how I tried to set up the problem.

I took the laboratory to be S and the frame of the particle whose speed we know to be S', so that the speed of S' relative to S is u = 0.65c.

Also, by convention, S' moves to the right of S, so that S moves to the left of S'.

Next, we know that the speed of particle two as viewed from particle 1's frame is ##v_x' = 0.95c##. So since we know ##v_x'## and are trying to find ##v_x##, I'd use equation 2. But this gives the wrong answer. If we use equation 1 we end up with the correct answer of 0.784c.

What are the official rules for doing this? How can I know when to use which, if I can't always go by the notation?

I took the laboratory to be S and the frame of the particle whose speed we know to be S', so that the speed of S' relative to S is u = 0.65c.

Also, by convention, S' moves to the right of S, so that S moves to the left of S'.

Next, we know that the speed of particle two as viewed from particle 1's frame is ##v_x' = 0.95c##. So since we know ##v_x'## and are trying to find ##v_x##, I'd use equation 2. But this gives the wrong answer. If we use equation 1 we end up with the correct answer of 0.784c.

What are the official rules for doing this? How can I know when to use which, if I can't always go by the notation?