A train moving with a speed of 54 m/spasses through a railway station at time t

Question

A train moving with a speed of 54 m/spasses through a railway station at time t = t' =0. Fifteen seconds later a firecracker explodes on the track2.3 km away from the train station in thedirection of that the train is moving. Find the coordinates of thisevent in both the station frame (consider this to be Home Frame)and the train frame. Assume that the train's direction of motionrelative to the station defines the x direction in bothframes.

station frame
x = 1 m
y = 2 m
z = 3 m
train frame
x' = 4 m
y' = 5 m
z' = 6 m

Explanation / Answer

In the station frame x = 2.3km                               y= 0km                               z= 0km In the train frame x1 = 2.3km -(0.054km/s)(15s)                               = 1.49km                           y1 = 0km                             z1=0km In the train frame x1 = 2.3km -(0.054km/s)(15s)                               = 1.49km                           y1 = 0km                             z1=0km

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