Learning Goal A rocket train car that is 30 m long is traveling from Los Angeles to New York at u = 0.5c when a light at the center of the car flashes. When the light reaches the front of the car, it immediately rings a bell. Light reaching the back of the car immediately sounds a siren. A bicyclist waiting to cross the tracks sees the light in front of her at the instant when it flashes. Are the bell and siren simultaneous events for the bicyclist? If not, what time delay does the bicyclist hear between the events?
Take the direction of motion of the train (eastward) to be the positive direction of x'. Let the instant when the light flashes be t0 s. What are (xA, tA) and (B, tB), the spacetime coordinates of event A and B in S?