Question

Relativity question: A meter stick in frame S makes an angle of 30° with the x axis. If that frame moves parallel to the x axis of frame S withspeed 0.90c relative to frame S, what is the length of the stick asmeasured from S?

Answer 1

The formula for space contraction is \[x'=x\sqrt{1-\frac{v^2}{c^2}}\]In this case:\[x'=x\sqrt{1-0.9}=x\sqrt{0.1}=\frac{x}{\sqrt{10}}\]The lenght of x=L cos(30°)=Lsqrt(3)/2\[x'=L\sqrt{\frac{3}{40}}\]And the new lenght is:\[L'=\sqrt{y^2+x'^2}=\sqrt{L^2 \sin^2 30°+L^2\frac{3}{40}}=L\sqrt{\frac{1}{4}+\frac{3}{40}}=L\sqrt{\frac{13}{40}}\]