Suppose that the velocity v of O relative to O is nearly that of light i.e., |v| = 1− where 0 < 1. Show that, (a) The time dilation formula reduces to ∆t ≈ ∆t √ 2 ; (b) The length contraction formula reduces to ∆x ≈ ∆x √ 2 ; (c) The velocity addition formula reduces to u ≈ 1 − 1 − w 1 + w ; (d) What are the relative errors on each of these approximations (parts (a)-(c)) when = 0.01 and w = 0.99
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