A train which is 300 m long in its frame is traveling north and comes to a tunnel that is 300 m long in the earth's ( the tunnel's) frame. If the back of the train reaches the south end of the tunnel at t' =0 and t = 0, how far out of the tunnel is the engine driver when the driver's watch says t' =0?
Observers are standing throughout the tunnel. Where is the observer ( i.e what is x) who observes the engine driver at t=0. What time does the driver's watch show to this observer?
If you do this correctly, you will have shown how the train can appear longer than the tunnel to people on the train and shorter than the tunnel to people in the tunnel.
Use x and x' of the rear of the train and station =0 at t'= 0,t=0. Thus x' of the engine driver is 300m and x of the tunnel north end is 300m.
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