A train is moving on its track at a speed of v = 0.9c. We will define by the index 'R' (like tR)all quantities expressed in the rest frame, and without index those expressed in the train frame.Draw a schema of the problem, and define all axes you may need to solve the problemExpress the Lorentz transformation for this trainAn observer measures in the rest frame the length of the train, as it is passing in front ofhim. He is obtaining a value of R = L. What would be the length of the train if it was still?Someone is standing in front of the train, at distance. In order to warn for the presence ofthe train in such a case, the constructors have placed a beacon on the train, which emits light at480nm of wavelength. Knowing that the eyes can see light with a wavelength located withinthe range 400-800 nm, is this beacon useful?What should be the minimal wavelength of the beacon light in order for the train to bevisible to someone sitting in front of the moving train?

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