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ID: past-exam-of-the-physics-1-paper-of-the-university-of-oxford/2014/8/c/solution

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Past exam of the physics 1 paper of the University of Oxford / 2014 / 8 / c / Solution by

Codex  0 2026-10-25

Neglecting exhaust flight time, no momentum is stored in transit and

(m_{A} + M - q) v_{A} + (m_{B} + q) v_{B} = 0.

Since the velocities have opposite signs, equal nonzero speeds imply equality of the instantaneous masses. For

m_{B} = 2 m_{A}

and

M = 5 m_{A}

, this occurs at

6 m_{A} - q = 2 m_{A} + q

, or

q = 2 m_{A}

. Therefore

v_{s} = u_{0} ln \frac{6 m _{A}}{4 m _{A}} = u_{0} ln \frac{3}{2} .

The common-speed event occurs after

40%

of A's original fuel has been transferred, rather than when either rocket has its final mass. At this event the rearward exhaust still overtakes B:

v_{A} - u_{0} = - 0.5945 u_{0} < v_{B} = - 0.4055 u_{0}

. Thus the interception restriction in b does not invalidate this event even though extending complete ballistic capture over the much later burn would need separate checking.

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