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homework5 - Homework Set 5 Due Thursday 07/28 1 Time...

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Homework Set 5 Due Thursday, 07/28 1. Time dilation and length contraction Problem 1: A spaceship travels from Earth to a star 100 light-years away. The ship is moving at a constant speed of 0.85 c . (a) How long does the trip take according to an observer on Earth? (b) How long does the trip take according to an observer on board the spaceship? (c) What is the distance from Earth to the star, according to the observer on the spaceship? Problem 2: Unstable particles are produced in a nuclear reaction in a laboratory. The particles have an average lifetime of 1.0 x 10 -10 seconds when at rest. The particles travel an average distance of 5 cm from the point of production before decaying, according to an observer at rest in the laboratory. What is the speed of the particles relative to the stationary observer? Problem 3: Suppose that at t = 0, Bob synchronizes his watch with Alice, and gets on a high-speed train that travels around and around the Earth at a speed of 500 km/h . If the train never stops, how long would Bob need to stay on it before his watch was off from Alice's by one second, due to time dilation? Express the answer in years. 2. Velocity addition Problem 4: Alice observes a particle moving with a speed of 0.8 c in the x direction, while Bob observes the same particle moving with a speed of 0.5 c in the x direction. How fast is Bob moving relative to Alice? Problem 5: An observer sees two spaceships, A and B , coming towards him from opposite directions with an equal speed. If the crew of ship A sees ship B approaching ship A at a speed of 0.9 c, what is the speed of the two spaceships relative to the observer?
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3. Lorentz transformation and 4-vectors Problem 6: Bob is moving in the x direction at a speed of 0.8 c relative to Alice. He detects two simultaneous explosions at t = 0. One explosion happens at position ( x, y, z ) = (10 6 km, 0, 0), while the other happens at ( x, y, z ) = (2 x 10 6 km, 0, 10 6 km). (a)
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This note was uploaded on 09/19/2011 for the course PHYS 1C taught by Professor Smith during the Spring '07 term at UCSD.

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homework5 - Homework Set 5 Due Thursday 07/28 1 Time...

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