 Solution

ID: past-exam-of-the-physics-1-paper-of-the-university-of-oxford/2017-resit/10/a/solution

Alison reaches the station at

t_{1} = 1/ (5/13) = 13/5

years. Her return worldline is

x_{A} = 1 - \frac{12}{13} (t - \frac{13}{5}) = \frac{17}{5} - \frac{12 t}{13},

while Belinda's is

x_{B} = - 5 t /13

. Equating them gives

T = \frac{221}{35} yr ≃ 6.3143 yr, x_{meeting} = - \frac{17}{7} ly .

This is the elapsed Earth-frame time, measurable by synchronized clocks in that inertial frame. A signal announcing the reunion reaches a clock physically on Earth later; its light-travel delay is not part of the requested frame-time comparison.

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