Circle Vacuum
How long? (Speed of light in vacuum)?
The vessels of the Solar Federation are marked with the symbol of the Federation, a circle, while the Empire Denebian vessels are marked with the symbol of the Empire, an ellipse whose major axis is n times its minor axis (a = nb in figure (Intro 1 figure)). FIGURE: http://session.masteringphysics.com/problemAsset/1011629/10/yf_Figure_37_24.jpg QUESTION: How fast, relative to an observer, Empire have a ship to travel for its brands to be confused with a Federation ship? Use c for the speed of light in a vacuum. _____________________________________________ **** The correct answer involves the variable n, which was not part of your reply.
x '= xSQRT (1 - V ^ 2 / c ^ 2) .... observed length contraction when an object is moving at the speed vx = rest length of major axis = number x = observed length of the main axis when the ship is traveling at speed v and must be equal to b, since you want to look like an ellipse Federation circle b = nb [SQRT (1 - v ^ 2 / c ^ 2)] (1 / n) ^ 2 = 1 - v ^ 2 / c ^ 2 v ^ 2 = (c ^ 2) [1 - (1 / n) ^ 2] = (c ^ 2) [(n ^ 2 - 1) / n ^ 2] v = (C / N) * SQRT [(n ^ 2 - 1)] You can see that if n = 1, which would mean that you start with a circle, then v = 0 since n ^ 2 - 1 is 0. As n becomes very large you can write that (c / n) n = c indicating that the ship could never travel faster than the speed of light.
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