Alice and Bob are passengers in a high-speed train moving at a uniform speed of v = c/2. Alice is at the rear of the train car and Bob is at the front of the car. The length of the car measured in their frame is L'. Alice throws a ball to Bob at speed u' = c/3.
a) In the frame of the train, how long does it take the ball to reach Bob?
b) In the frame of the station, how long does it take the ball to reach Bob?
c) In the frame of the ball, how long does it take the ball to reach Bob?
d) Verify that the proper time between Alice throwing the ball and Bob receiving it is the same in all three frames.

You have two photos of a person walking. one shows the person at the corner of third and main streets, the other shows the person at the corner of tenth and main streets. there are lampposts at every corner in this town, and the first picture shows it to be 10: 32: 00 exactly. the second picture shows it to be 10: 49: 30. you know three facts: (1) all of the clocks are synchronized; (2) there are exactly 12 equal-sized blocks per kilometer in this town; and (3) the streets that cross main in this area are numbered consecutively, with no interruptions. what is the person’s average speed in kilometers per hour?