Question

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

Answer 1

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