Past exam of the mathematics course of the University of Cambridge / 2006 / ib / Paper 4 / 17B / a

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- Solution a

Solution

The Lorentz factor for

β = v / c = 12/13

is

γ = \frac{1}{1 - β ^{2}} = \frac{13}{5} .

The javelin's length at simultaneous barn-frame times follows from length contraction:

L_{javelin} = \frac{4}{γ} = \frac{20}{13} m .

Its proper length remains four metres.

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