The Kingston-Oshawa Train Our good old friend, the high-speed train from Kingston to Oshawa, needs a better communication system. As a first step,...

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The Kingston-Oshawa Train Our good old friend, the high-speed train from Kingston to Oshawa, needs a better communication system. As a first step, precise clocks are installed at the stations in Kingston andOshawa, which emit regular electromagnetic signals (so the signals move with the speed of light)every 0.20 ms, starting at time 0. The same type of clock is also installed in the train. The clocksat the stations are synchronized and they show I = 0 at the moment the train leaves the Kingston station towards Oshawa with a speed of 0.60 c. The train’s clock shows 13’ = 0 at this verymoment as well. Oshawa is (still) 180 km away from Kingston (in the positive x-direc‘tion), as measured by somebody at rest relative to the station. Kingston is the origin of the referenceframe that is at rest relative to the stations. The clock on the train marks the origin of the train’sreference frame. We identify a number of events: so,” and .9092: the first and second signal is emitted by the Oshawa station 3M1 and .9382: the first and second signal is emitted by the Kingston station 31-91 and 37-92: the first and second signal is emitted by the train eon and so”: the first and second signal from the train is received by the Oshawa station3K” and .9ng: the first and second signal from the train is received by the Kingston stationand and or”: the first and second signal fi'om the Kingston station is received by the train a) Calculate the time and position of all the above events in both reference flames (give the timein ms and the position in km). In all cases: first calculate the respective coordinates in one ofthe two frames (the one in which you think the respective coordinates are more easilydetermined) and then use the Lorentz Transformation equations to convert to the otherreference frame. b) Calculate the time difference between the arrival times at each of the three location (in therespective reference fi'ame where the signals arrive). c) Draw spacetime diagrams for both reference frames including the train, the stations and allrelevant signals. Label all world lines and all above events.