Past exam of the physics course of the year 1 of the natural sciences course of the University of Cambridge / 2024 / Paper 1 / Section B / 7 / a

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- Solution a

Solution

The collinear relativistic velocity addition formula is

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

With both velocities directed toward Earth,

u = \frac{0.6 c + 0.8 c}{1 + 0.48} = \frac{35}{37} c = 0.946 c .

The denominator keeps the result below

c

. Adding the two speeds by the Galilean rule would give an inadmissible

1.4 c

.

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