Chapter 2, Problem 94E

A kaon (denoted $K^0$ ) ¡s an unstable particle mass $8.87\times {10}^{-28}kg$ . One of the means by which it decays is by spontaneous creation of two pions, a ${\pi }^{+}$ and ${\pi }^{-}$ . The decay process may be represented as
$K^0\to {\pi }^{+}+{\pi }^{-}$

Both the ${\pi }^{+}$ and ${\pi }^{-}$ have mass $2.49\times {10}^{-28}kg$ . Suppose that a kaon moving in the $+x$ direction decays by this process with the ${\pi }^{+}$ moving off at speed 0.9c and the ${\pi }^{-}$ at 0.8c. (a) What was the speed of the kaon before decay? (b) In what directions do the pions move after the decay?