 Solution

ID: past-exam-of-the-short-options-course-of-the-university-of-oxford/2023/8/c/solution

u = \frac{c /2 - ( - c /2 )}{1 - ( c /2 ) ( - c /2 ) / c ^{2}} = \frac{4 c}{5} .

γ = (1 - u^{2} / c^{2})^{- 1/2} = 5/3

. By length contraction, the spatial length measured at simultaneous times in that rocket's rest frame is

L = L_{0} / γ = 3 L_{0} /5 .

This is the inertial-frame length measurement; a visual image assembled from light arriving at one instant is a different measurement.

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