A rocket train car that is 30 m long is traveling from Los Angeles to New York at v=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?
(1.) Let S be the reference frame of the bicyclist. Which other frame listed below provides useful information to solve this problem?
A) the reference frame of an observer that is stationary in Los Angeles
B) the reference frame of an observer at rest relative to the Sun
C) the reference frame of an observer that is stationary in New York
D) the reference frame of a passenger in a seat near the center of the train (CORRECT ANSWER)
(2.) Choose frame S' so that its origin is located at the center of the train. Take the direction of motion of the train (eastward) to be the positive direction of x'. Let the instant when the light flashes be t'=0s. What are (x'A,t'A) and (x'B,t'B), the spacetime coordinates of event A and B in S'? Note that the time coordinate of an event is the time at which the event actually occurs, not the time at which an observer receives information about it (e.g. when a passenger hears the sound of the bell or the siren).
(x'A,t'A), (x'B,t'B) = [15.0,5.00*10^(-2),-15.0,5.00*10^(-2)] m,μs, m,μs (CORRECT ANSWERS)
(3.) What is the time interval Δt=|tA−tB| between events A and B when measured in S?
Δt = 5.77×10^(-2) μs (CORRECT ANSWER)
(4.) How long (L) is the train according to the bicyclist?
L = m (I have all of the answers except for 4. LOOKING FOR THE ANSWER PLEASE) - Thank you :)