 Solution

ID: past-exam-of-the-physics-1-paper-of-the-university-of-oxford/2013/10/b/solution

The berth moves at

0.85 c

in the ship's initial rest frame, so it too is subject to length contraction:

L_{b}^{'} = \frac{L _{b}}{γ _{s}} = 100 (1 - 0.8 5^{2}) + 4 1 - 0.8 5^{2} ≃ 29.8571 m .

The ship remains

100 m

long in this frame. The two length comparisons use different simultaneous endpoint events; this is the same relativity of simultaneity that resolves the ladder paradox. Physical docking also requires deceleration, whose later effects are outside these initial inertial measurements.

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