USAPhO 2012 Semi-Final Problem A1

A newly discovered subatomic particle, the S meson, has a mass M. When at rest, it lives for exactly \tau=3 \times 10^{-8} seconds before decaying into two identical particles called P mesons (peons?) that each have a mass of \alpha M.

a. In a reference frame where the \mathrm{S} meson is at rest, determine
i. the kinetic energy,
ii. the momentum,
iii. the velocity
of each \mathrm{P} meson particle in terms of M, \alpha, the speed of light c, and any numerical constants.

b. In a reference frame where the \mathrm{S} meson travels 9 meters between creation and decay, determine
i. the velocity
ii. kinetic energy of the \mathrm{S} meson.

Write the answers in terms of M, the speed of light c, and any numerical constants.