 Solution

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

The velocity-addition formula combines the ship's station-frame velocity and the capsule's ship-frame velocity:

\frac{v _{c}}{c} = \frac{0.85 + 0.9}{1 + 0.85 ( 0.9 )} = \frac{350}{353} ≃ 0.9915014.

For the distance convention in i, station-frame arrival takes

D / v_{c} = (353/350) day = 1.008571 day

. Transforming its two endpoint events back to the ship frame gives

γ_{s} [D / v_{c} - 0.85 D / c]

, agreeing with i. The capsule remains below the speed of light in either frame.

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