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Relativity Homework #3
1. Abram and Jarnia are at it again. Abram’s battle cruiser moves directly toward Jarnia’s
super secret scout ship when Abram fires a decoy toward the scout ship. Relative to the scout
ship, the speed of the decoy is 0.980c and the speed of Abram’s cruiser is 0.900 c. What is the
speed of the decoy relative to the cruiser?
2. a. In terms of c, what is the speed of an electron whose kinetic energy is 100 MeV?
b. Find the speed and the Lorentz factor  for a proton whose kinetic energy is 1.00 keV.
c. for the protons at FermiLab, whose energies are > 500 GeV?
3. Quasars are thought to be the nuclei of active galaxies in the early stages of their formation.
A typical quasar radiates energy at the rate of 1041 Joules/second. At what rate is the mass of
this quasar being reduced to supply this energy? Express your answer in solar mass units per
year, where the solar mass is 2.0 x 1030 kg.
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4. In a high-energy collision between a cosmic-ray particle and a particle near the top of the
earth’s atmosphere, 120 km above sea level, a pion is created. The pion has a total energy of
1.35 X 105 MeV and is traveling vertically downward. In the pion’s rest frame, the pion decays
35.0 ns after its creation. At what altitude above sea level, as measured from the earth’s
reference frame, does the decay occur? The rest energy of a pion is 139.6 MeV.
5. David, who as we all know, is in his own galaxy, Galaxy A, recedes from us in our Milky
Way at 0.35 c. Ovi is in Galaxy B and is located in precisely the opposite direction and is also
found to be receding from us at 0.35 c. What recessional speed would David compute for us?
and what speed would he compute for Ovi?
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