Video Problem #1, Lecture #12: At time t = 0, the center of a train passes a station (located at x = 0), travelling at a speed v = 0.5c in the +x direction. Fred is standing next to the track at the station, and Wilma is riding on the train at the center. At t = 4 μs, Fred drops a hammer on his foot. At t = 6 μs, he sees Wilma light a match in the train.

a. Draw a space-time plot for this scenario. On the plot, draw and label: (i) Fred’s and Wilma’s world lines (label them “Fred” and “Wilma,” respectively (make sure Wilma’s world line accurately shows her speed); (ii) the world line for the light from the match as it travels toward Fred (label as “light”); and (iii) the two events: M = Wilma lights Match, and H = Fred drops Hammer.

b. From Fred’s (the station’s) reference frame, what is the ordering of the events H and M? (Does M come first, H come first, or are the events simultaneous?) Show and/or explain how you determined your answer.

c. From Wilma’s (the train’s) reference frame, what is the ordering of the events M and H? Use the space-time diagram to show how you determined your answer.