# Speed of light question

#### RRR

not sure if this is the right place to post this question. If not, please forgive me.

I have no training in physics so this may seem like a silly question and I'm sure a similar if not identical analogy exists. But here goes.

Train A is travelling at 60% the speed of light going East. Train B is approaching Train A while also travelling at 60% the speed of light going West. Train A is equipped with a trip wire at the front and a trip-wire at the back and also a light at the front of the train and a light detection device at the back. When the front of Train A meets the plane of the front of Train B, the first trip wire sets of the light at the front of train A. The question is, will Train B make it to the rear of train A before the light?

Remember, I'm just a duffer so take it easy on me

Robert

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#### RRR

here is a crude diagram of my question

see attachment

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• 10.4 KB Views: 266

#### jcsd

Gold Member
Firstly I assume you mean from the refernce point of train A (though this won't affect the answer qualitvely). The answer is no the light will always reach there first as in special relativty the velocites do not sum in the same way they do in Galliean relatvity, but obey the formula v' = (u + v)/(1 + uv/c2), so, from the point of view of train A, train B will be travelling at about 88% of the speed of light and (by symmetry) vice versa.

#### RRR

Thank you...Yes, it was from Train A that I was thinking.

Now, for the full force of my ignorance. "u" represents what? And which velocity does "v'" and "v" represent?

Thanks again,
Robert

#### jcsd

Gold Member
In this case u represents the velocity of Train A from the refernce point of the track, v the velocity of Train B from the refernce point of the track and v' the velocity of Arain B from the reference point of Train A

#### RRR

many thanks again

thanks for the help,
Robert

#### mtworkowski@o

Re: here is a crude diagram of my question

I see that even some "duffer"s have many brain cells. That was very well done.

#### mtworkowski@o

I'm going to stick my neck out and say this: If you watch the strobe light on a plane at nite, you basically see the flash and then in another location you see another flash. Now the plane is moving but the light isn't. Imagine that a light source is sending out many flashes instead of one continuous stream. And each flash stays where it was when it was created. And emanates from that point. That, I think is what light does. In the train analogy, the tracks would be the ref frame. It's like taking a snapshot of the trains.
Now I'll wait for everybody to land on me.
Regards.

#### paw

The question is, will Train B make it to the rear of train A before the light?
As already answered, yes, the light will arrive at the detector before Train B. Here's a spacetime diagram showing the result diagrammatically from the rest frame of Train A.

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