Do Firecrackers Explode Simultaneously on a Moving Train?

[explodingbird]

Homework Statement

Two firecrackers explode simultaneously 125 m apart along a railroad track, which we can take to define the x-axis of an intertial reference frame. A train (the other reference frame) moves at a constant 25 m/s in the +x direction relative to the track frame.

a) According to the galilean transformation equations, do the firecrackers explode at the same time?
b) How far apart are the explosions as measured by the train frame?
c) Assume that instead of the explosions being simultaneous, the firecracker farther ahead in the +x direction explodes 3.0 s before the other. How far apart would the explosions be as measured in the train frame?

Homework Equations

t'=t
x'=x-vt
y'=y
z'=z

The Attempt at a Solution

For part a, the answer would be yes.

For part b, I am having trouble using the equation x'=x-vt. I understand that v = 25, but I'm confused as to what t I'm supposed to plug in and what x value.

 

[Pi-Bond]

You would need to assign a coordinate system in which both frames have coinciding origins at t=0 to use the transformations. The question doesn't say anything about the position of the train when the firecrackers explode. You could say that it is at the same point as the first firecracker so that x=x'=0 at t=t'=0. Using that you can find the spatial distance of the events in the train frame (the x coordinate of the other cracker can be found from the given distance)

 

[Redbelly98]

Moderator's note:

I have moved this thread to "Introductory Physics". "Advanced Physics" is meant for college junior-level courses and beyond. Galilean and special relativity are typically taught before that.