The crew in rocket 1 was performing an experiment with kaons, K degree , which d
ID: 1482024 • Letter: T
Question
The crew in rocket 1 was performing an experiment with kaons, K degree , which decay to two charged pions, K degree right arrow phi^+ phi^-. What are the three- momenta and the energies of the decay products (the two pions) as measured by the crew in rocket 1, if kaon is at rest in rocket 1? The mass of the kaon is mK = 0.497GeV/c2, and of the pion mphi = 0.140GeV/c2. What are the three-momenta and the energies of the pions as viewed from rocket 2, if the pions travel perpendicular to the rockets' flight directions, or parallel to the rockets' flight direction? If each of the crews on rockets have 50min to evacuate (in their proper time), will they be able to leave the respective rockets before the collision? The initial distance between the rockets as viewed from earth is 9.1011m. Calculate the time each of the crews have before the collision (in their respective frames).Explanation / Answer
K0 --------> pi+ pi-
rest mass of K+ mk = 0.497 GeV/c2 and pion mpi = 0.140 GeV/c2
speed of the rocket v= 0.7 c
reduction factor , g = 1/ sqrt ( 1 - v2/c2)
g = 1/ sqrt ( 1 - (7c)2/c2 )
g = 1.4
E2 = p2c2 + m02c4
p2c2 = g E02 - m02c4
= g m02c4 - m02c4
p = sqrt ( m02c2 (g -1) )
for K+ , pk+ = sqrt { 0.4972 x 3x1082 ( 1.4 -1) }
pk+ = 9.43 x107 GeV/C
for pi+ and pi- , ppi = sqrt { 0.1402 x 3x1082 (1.4 -1) }
ppi = 2.66x107 GeV/C
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