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Unformatted text preview: 79. We refer to the particle in the ﬁrst sentence of the problem statement as particle 2. Since the total
momentum of the two particles is zero in S , it must be that the velocities of these two particles are
equal in magnitude and opposite in direction in S . Letting the velocity of the S frame be v relative to
S , then the particle which is at rest in S must have a velocity of u1 = −v as measured in S , while the
velocity of the other particle is given by solving Eq. 38-28 for u :
u2 = c
u2 − v
1 − u2 v/c2
1 − 2 cv
2 . Letting u2 = −u1 = v , we obtain
2 1− c
c2 = v =⇒ v = c(2 ± √ 3) ≈ 0.27c where the quadratic formula has been used (with the smaller of the two roots chosen so that v ≤ c). ...
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