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Questions from Relativity

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1. “After the Sun, the nearest star visible to the naked eye is Rigel Centaurus, which is 4.35 light years away. If a Spacecraft was sent there from earth at a speed of 0.80c, how many years would it take to reach that star from earth as measured by observers (a) On Earth; (b) On the Spacecraft? (c) What is the distance travelled according to observers on the spacecraft?”
2. A beam of a certain type of elementary particle travels at a speed of 2.58 x10^8 m/s. At this speed, the average lifetime is measured to be 2.50 x 10^-8 s. What is the particles lifetime at rest?
3. Imagine a rocketship takes off for a distant planet and can travel at many times the speed of light. (We know that this is impossible but let’s just say you can for this question). Observers on the planet are viewing the incoming spaceship through a powerful telescope. Describe what they will see from the moment the rocketship leaves Earth until it land on the observer’s planet. Support your answer with example equations.
4. If you were on a rocketship travelling at 0.6c away from the sun, at what speed would the sunlight pass you?
5. A 100 MeV electron, travelling at 0.999987c, moves along the axis of an evacuated tube that has a length of 3.00m as measured by a laboratory observer S with respect to whom the tube is at rest. An Observer S0 moving with the electron, however, would see this tube moving past her. What length would the tube appear to the Observer?

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