Question

Space cruisers A and B are moving parallel to the positive direction of an x axis. Cruiser A is faster, with a relative speed of v 0.946c, and has a proper length of L 255 m. According to the pilot of A, at the instant (t=0) the tails of the cruisers are aligned, the noses are also. According to the pilot of B, how much later are the noses aligned? Draw a diagram.

Answer 1

The relative speed of A is v_A=0.946c and its proper length Lo=255 m, then you should find the length that B is observing,
\[L=L_0\sqrt{1-(0.946)^2}=82.66 m\]
Then, the time that B measures is,
\[\Delta t=\frac{L_0-L}{v_A}=6.08\cdot10^{-7}s\]