Solving Physics Problem Involving Time Dilation and Length Contraction

[VenomHowell15]

Homework Statement

Two lightning bolts strike the ends of a moving boxcar (Points A and B). The boxcar has length 2d and is moving at a speed v. A stationary observes both lightning bolts hitting the boxcar simultaneously. An observer in the car, however, claims that the front (position B') of the boxcar was hit first, then the back (position A'). The light takes t=d/c to reach a stationary observer O. If the boxcar moves distance l in this time, calculate the time for the light from both A' and B' to reach observer O', who is in the middle of the boxcar. Express your answers in terms of c, d, and l.

Homework Equations

Not entirely sure.

t' = yt perhaps?

The Attempt at a Solution

Alright... I've JUST started modern physics to be honest, and it's a radical departure from what I've learned before and I find myself at a complete loss as to how to approach this question. Can anyone perhaps give me a nudge in the right direction? Is this a time dilation or length contraction question? Perhaps both?

I've tried to use t' = yt, but I'm just not sure how to take into account the car moving toward or away from the light source. Would the end result for the time for the observer inside the car essentially t +- t'? I have no idea.

I went through the calculations, making sure everything was in terms of c, d, and l, and I came up with something along the lines of
\Deltat'=\frac{d}{c\sqrt{1-\frac{l^2}{d^2}}}

But this really doesn't help me, to my knowledge.

 

[Doc Al]

You just need to find the times (according to the stationary observers) that the light from each lightning strike hits the moving point O'. No need for any fancy time dilation or length contraction, just the fact that the speed of light is always c and that distance = speed*time. Hint: Express the speed of the train in terms of c, d, and l.

 

[VenomHowell15]

You just need to find the times (according to the stationary observers) that the light from each lightning strike hits the moving point O'. No need for any fancy time dilation or length contraction, just the fact that the speed of light is always c and that distance = speed*time. Hint: Express the speed of the train in terms of c, d, and l.

Yeah, I'm getting that the speed of the train is (lc)/d given the relevant information, I'm just not entirely sure how to factor this into figuring out the time it takes for either lightning bolt to reach observer O'. I'm probably not thinking about this in the correct mindset...

 

[Doc Al]

So far, so good. Consider this: At the instant (according to the stationary observers) that lightning strikes point B, O' and B are a distance d apart. You know the speed of O' and the speed of light, so figure out when they meet. (Simple kinematics.)

 

[VenomHowell15]

So far, so good. Consider this: At the instant (according to the stationary observers) that lightning strikes point B, O' and B are a distance d apart. You know the speed of O' and the speed of light, so figure out when they meet. (Simple kinematics.)

I guess when you put it like that, it seems rather simple... Perhaps I'm just trying to complicate things more, but I figured this would be an issue of time dilation considering it's a problem we were given in our first chapter of Modern Physics, which deals with time dilation and length contraction and the like.

So, would the answer for t be something like (lc +- cd)/(d^2)? The +- of course depending on whether we're referring to point A' or point B'

 

[Doc Al]

Don't worry, you'll get to that more interesting stuff quick enough. This kind of reasoning is essential to understanding some of the relativistic thought experiments and derivations.

 

[VenomHowell15]

Don't worry, you'll get to that more interesting stuff quick enough. This kind of reasoning is essential to understanding some of the relativistic thought experiments and derivations.

Just a quick check though. I think I edited my reply when you were writing yours. Am I looking for an answer something along the lines of t = (v +- c)/(d) = ([lc]/d +- c)/d = (lc +- cd)/(d^2)?

 

[Doc Al]

Am I looking for an answer something along the lines of t = (v +- c)/(d) = ([lc]/d +- c)/d = (lc +- cd)/(d^2)?

On the right track, but you mixed it up a bit. In one case: d = ct + vt; in the other: d = ct - vt.

 

[VenomHowell15]

On the right track, but you mixed it up a bit. In one case: d = ct + vt; in the other: d = ct - vt.

Very amateurish mistake by me, really... I know the difference, just kind of messed up in the way I was writing it out. Ended up with the inverse of the time rather than time :p