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14 Nov 2019
Consider two identical length rockets, A and B, moving in the same direction in interstellar space. An observer on board either rocket measures its length at rest to be L. A referee outside the rockets measures the speed of rocket A to be vA, and the speed of rocket B to be vB, where vA > vB. At t = 0 according to clocks on board A and B as well as the referee, the front of both rockets line up together. They move towards a finish line a distance R away, as measured by the referee. The referee uses a movie recorded in his frame at the finish line to measure how many rocket lengths separate the two spaceships as the front end of A crosses the finish line. The measurement is made from the front of rocket A to the front of rocket B. How many lengths does he measure using the length of A as measured in his frame? Using the length of B as measured in his frame? Do observers A and B agree with the referee in their measurements? If so, why? If not, why not?
Consider two identical length rockets, A and B, moving in the same direction in interstellar space. An observer on board either rocket measures its length at rest to be L. A referee outside the rockets measures the speed of rocket A to be vA, and the speed of rocket B to be vB, where vA > vB. At t = 0 according to clocks on board A and B as well as the referee, the front of both rockets line up together. They move towards a finish line a distance R away, as measured by the referee. The referee uses a movie recorded in his frame at the finish line to measure how many rocket lengths separate the two spaceships as the front end of A crosses the finish line. The measurement is made from the front of rocket A to the front of rocket B. How many lengths does he measure using the length of A as measured in his frame? Using the length of B as measured in his frame? Do observers A and B agree with the referee in their measurements? If so, why? If not, why not?