A 40-m-long rocket train car is traveling from L.A. to N.Y. at 0.60c when a ligh

Question

A 40-m-long rocket train car is traveling from L.A. to N.Y. at 0.60c 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. A passenger seated in the train car says that the siren sounds at time t=0. What time does the passenger say the bell rang? Use negative times if the bell rings earlier.




b. A bicyclist is waiting to cross the tracks and measures that the siren sounds at t=0. What time does the bicyclist say that the bell rings? Again, use negative times if the bell rings earlier.

please help me out for part b

Explanation / Answer

hi, this is a same question with just different numericals .I am posting both question and answer. Also it may serve well and be helpful to you if you practice on your own . :)Please rate me Lifesaver !!!!

Events in the car are simultaneous for an observer in the car- the wave front reaches the front and the
back of the car simultaneously.
Simultaneous events in one frame are never simultaneous in aframe moving with respect to the frame
in which the simultaneous events occur
t2 = [t1 - vx1 / c2] / (1 - v2 /c2)
t1 = 0 the events aresimultaneous
x1 = 30 m the events occur30 m apart in the train
1 / (1 - v2 / c2) = 1 / (1- .64) = 1.67
t2 = 1.67 * .8 c * 30 / c2 = 13.3= 40.1 / 3 * 10E8 = 1.34 * 10E-7 sec
Note: t2 is negative and the siren ringsbefore the bell sounds.
This makes sense because an observer on the groundopposite the light in the middle of the car
would see the back of the car approaching the wavefront whilethe front of the car would be receding from the wavefront.

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