 Solution

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

Using

v / c = tanh θ

\frac{v ^{''}}{c} = tanh (θ + θ^{'}) = \frac{v / c + v ^{'} / c}{1 + v v ^{'} / c ^{2}} .

v^{''} = \frac{v + v ^{'}}{1 + v v ^{'} / c ^{2}} = \frac{c ^{2} ( v + v ^{'} )}{c ^{2} + v v ^{'}} .

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