Physics 215 Homework Set 1 1.A spaceship of length 40m at rest is observed to be 20m long when in motion. How fast is it moving? Hint: derive a formula giving βin terms of γand put it on your formula sheet.
2.The Concorde travelled 8000 km between two places in North America and Europe at an average speed of 375 m/s. What is the total difference in time between two similar atomic clocks, one on the airplane and one at rest on Earth during a one-way trip? Consider only time dilation and ignore other effects like the rotation of the Earth. Hint: you will need the binomial expansion (see algebra above Eq 35.4)
3.A spaceship is moving at a speed of .8c away from Bob, at rest. Alice, in the spaceship, shoots a proton gun with protons having a speed of 0.7c. What is the speed of the protons measured by Bob when the gun is shot (a) away from Bob and (b) towards Bob? . Use the velocity addition formulas. 4.. Two events occur in an inertial system K at the same time, but 4km apart. What is the time difference measured in a system K’ moving parallel to these two events when the distance separation of the events is measured to be 5km in K’?