IB Physics HL A 5 6 Hl Lorentz Transformations Topic Practice

An observer P sitting in a train moving at a speed v measures that his journey takes a time $\Delta t_{\mathrm{p}}$. An observer Q at rest with respect to the ground measures that the journey takes a time $\Delta t_{\mathrm{Q}}$.

According to Q there is an instant at which the train is completely within the tunnel. At that instant two lights at the front and the back of the train are turned on simultaneously according to Q .

The spacetime diagram according to observer Q shows event B (back light turns on) and event F (front light turns on).

Apply a Lorentz transformation to show that the time difference between events B and F according to observer P is $2.5 \times 10^{-7} \mathrm{~s}$.