Special Relativity | Part IB, 2002

Write down the formulae for a Lorentz transformation with velocity vv taking one set of co-ordinates (t,x)(t, x) to another (t,x)\left(t^{\prime}, x^{\prime}\right).

Imagine you observe a train travelling past Cambridge station at a relativistic speed uu. Someone standing still on the train throws a ball in the direction the train is moving, with speed vv. How fast do you observe the ball to be moving? Justify your answer.

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