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In an "atom smasher," two particles collide head on at relativistic speeds. If the velocity of the first particle is 0.741c to the left, and the velocity of the second particle is 0.543c to the right (both as Measured in the lab rest frame) , how fast are the particles moving with respect to each other?


A) 0.834c
B) 0.934c
C) 0.916c
D) 1.284c

E) A) and C)
F) A) and D)

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A spaceship with a constant speed of 0.800c relative to Earth travels to a star that is 4.30 light-years from Earth. How much time for this trip would elapse on a clock on board the spaceship?


A) 5.38 y
B) 3.23 y
C) 5.15 y
D) 4.40 y

E) A) and B)
F) C) and D)

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An astronaut on a spaceship moving at 0.927c says that the trip between two stationary stars took 4.26 y. How long does this journey appear to take to someone in the rest frame of the two stars?


A) 1.60 y
B) 2.30 y
C) 12.6 y
D) 11.4 y

E) None of the above
F) A) and D)

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Calculate the amount of energy needed to accelerate an electron from 0.888 c to 0.991 c. Express your answer in MeV. The rest mass energy of an electron is 0.511 MeV.


A) 2.71 MeV
B) 1.90 MeV
C) 5.69 MeV
D) 4.61 MeV

E) B) and D)
F) B) and C)

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A spaceship enters the solar system moving toward the sun at a constant speed relative to the sun. By its own clock, the time elapsed between the time it crosses the orbit of Jupiter and the time it crosses the orbit of Mars is 50.050.0 minutes. As measured in the coordinate system of the sun, how Iong did it take for the spaceship to travel that distance? The radius of the orbit of Jupiter is 778×778 \times 109 m10 ^ { 9 } \mathrm {~m} , and that of the orbit of Mars is 228×109 m228 \times 10 ^ { 9 } \mathrm {~m} .


A) 58.658.6 minutes
B) 30.030.0 minutes
C) 95.895.8 minutes
D) 69.869.8 minutes
E) 43.643.6 minutes

F) None of the above
G) B) and E)

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A really high-speed train moves in a direction parallel to its length with a speed that approaches the speed of light. The height of the train, as measured by a stationary observer on the ground,


A) increases slightly.
B) decreases slightly.
C) approaches infinity.
D) approaches zero.
E) does not change due to the motion.

F) A) and D)
G) A) and C)

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