Chapter 2, Problem 32E

You are on a high−speed train, traveling at a decent clip: 0.8c. On the ground are two signal stations 5 km apart, each with a status−reporting sign, which always give simultaneous reports. At precisely noon on the train’s clocks, the conductor at the front of the train passes one station and sees a sign reading “All Clear,” and another employee at the back passes the other station and sees a sign reading “Severe Electrical Storms Reported! Slow to 0.1c!” (a) How long is the train? (b) Should it slow down? (c) Suppose that both reporting signs display the time very precisely, updated every microsecond. By how much would the two observed time readings differ, if at all?