# What should the speed of a pion be

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1. Feb 15, 2017

### annalian

1. The problem statement, all variables and given/known data
The speed of a particle in Earth's frame is 0.4 c. A second particle goes away from the first one with speed 0.6 c. What is the speed of the second particle in Earth's frame?

2. Relevant equations
u=(u'+v)/(1+u'v/c^2)

3. The attempt at a solution
I think v=0.4 c and u'=-0.6, but as I use the above equation the solution is not 0.8 c(as it is in my book). If I put v=-0.6 and u=0.4 then the solution is 0.8 c. Which one is correct?

Last edited: Feb 15, 2017
2. Feb 15, 2017

### kuruman

I have a hard time figuring out what primes and unprimes and u's and v's all mean. That's why with problems like this I use the double subscript method.
Let
VAE = velocity of object A relative to E (E stands for Earth)
VBE = velocity of object B relative to E
VBA = velocity of object B relative to A
$$V_{BE}=\frac{V_{AE}+V_{BA}}{1+V_{AE}V_{BA}/c^2}$$
The mnemonic is that you add together the velocities that have the same subscript appearing both on the left and the right. In this case this subscript is "A". Once you set up the equation this way, you substitute the numbers and solve for the unknown which might or might not be on the left side of the equation.

3. Feb 15, 2017

### annalian

I did it and vBE=-0.26c, not 0.8c as written in the book

4. Feb 15, 2017

### kuruman

Your difficulty is in the above statement which is ambiguous. Imagine yourself being an observer sitting on particle A. There are two possibilities
1. You see B ahead of you "going away at speed 0.6c" in which VBA = +0.6c
2. You see B behind you "going away at speed 0.6c" in which VBA = -0.6c

Given the wording of the problem either answer can be correct. The problem should have given a velocity, not a speed.