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βI solved this problem but I do not know if it is correct becasue there is no way to check it:

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

Use Galilean transformation equations for position. β is the contstant velocity.

t=t'

x'=X- β*t

Here is my work: 25m/s*12s=300m

300m+120m= 420m

Train Frame 420m

420m=X-300m

X=720m

Track frame 720m

Is this correct?

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

## Homework Equations

Use Galilean transformation equations for position. β is the contstant velocity.

t=t'

x'=X- β*t

## The Attempt at a Solution

Here is my work: 25m/s*12s=300m

300m+120m= 420m

Train Frame 420m

420m=X-300m

X=720m

Track frame 720m

Is this correct?

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