Imagine that we define the rear end of a train 120 m long to long to define the origin X'=0 in the train frame and we define a certain track signal light to define the origin X=0 in the track frame. Imagine that the rear end of of the train passes this sign at t+t'=0 as the train moves in the +X direction at a constant speed of 25 m/s. 12 seconds later, the engineer turns on the train's heasdlight.
A) Where does this event occur in the train frame?
B) Where does this event occur in the track frame?