# Special relativity velocity tansforms

1. May 21, 2008

### Vuldoraq

[SOLVED] Special relativity velocity tansforms

1. The problem statement, all variables and given/known data

A $$K^{0}$$ meson at rest decays into a $$\pi^{+}$$ meson and a $$\pi^{-}$$ meson, each having a speed of 0.85c.

If the K0 meson is travelling at 0.9c when it
decays, what is the greatest speed that one of the $$\pi$$ mesons can have?

What is the least speed?

2. Relevant equations

$$v_{x}=v_{x}^{'}+u/(1+u.v_{x}^{'}/c^{2})$$

3. The attempt at a solution

I am a bit stuck when it comes to putting what values where. I think that to find the maximum speed the pions will be in the same direction as the meson, and to find the minimum speeds the pions will be moving in the opposite direction to meson. However I don't really know what speed to put where or if I'm even barking up the right tree.

Last edited: May 21, 2008
2. May 21, 2008

### Vuldoraq

Ok, I've done some calculations please could someone tel me if they are right?

Letting $$v_{x}^{'}=0.85c$$ and $$u=0.9c$$ and applying the above formula
in its form gives,

$$v_{x}=0.99c$$ as the maximum velocity.

Then,

Letting $$v_{x}^{'}=-0.85c$$ $$u=0.9c$$ and applying the above formula
in its form gives,

$$v_{x}=0.21c$$ as the minimum velocity.

does this look reasonable?

3. May 21, 2008

right