Exam 26: The Special Theory of Relativity

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?

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?

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 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,

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 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 $50.0$ 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 $778 \times$ $10 ^ { 9 } \mathrm {~m}$ , and that of the orbit of Mars is $228 \times 10 ^ { 9 } \mathrm {~m}$ .