# Special relativity velocity tansforms

[SOLVED] Special relativity velocity tansforms

## Homework Statement

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?

## Homework Equations

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

## 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.

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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?

right