(Solved): Exercise 7 - Time dilation / Length contraction (25\%): An observer \( P \) stands in the middle o ...

Exercise 7 - Time dilation / Length contraction (25\%): An observer \( P \) stands in the middle of a train station platform as a high-speed train passes oy at \( v / c=0.8 \). The observer \( P \), who measures the platform to be \( 60 \mathrm{~m} \) long, notices that he front and back ends of the passing train line up exactly with the ends of the platform at the same time. 1. [5\%] How long (in [s]) does it take for the whole train to pass \( P \) as he stands on the platform, as measured by his watch? 2. [5\%] According to a rider T on the train, how long (in [m]) is the train? 3. [5\%] According to a rider T on the train, what is the length (in [m]) of the platform? 4. [5\%] According to a rider T on the train, how long (in [s]) does it take for the whole train to pass observer \( \mathrm{P} \) standing on the train station platform? 5. [5\%] According to a rider \( T \) on the train, the ends of the train will NOT simultaneously line up with the ends of the platform (contrary to what \( P \) observes). What time interval (in [s]) does T measure between when the front end of the train lines up with the front end of the platform, and when the back end of the train lines up with the back end of the platform? [Hint: a sketch of the scene can help!]