Undergrad Solving Special Relativity Problem w/ Two Spaceships

[universal2013]

Hello there. In class, our teacher solved one question and asked us what did we wrong specifically in the solution because there were two sets of them. Two spaceships are moving through +x and -x and there is a distance L between them. From one observer which is stationary in the line of L/2 sees both spaceships move with 0.5 c and they will collide in some time. We find the collision time dL/dt = -[0.5c+0.5c] = c
and from spaceships' reference frame we find the velocity of the second spaceship with Lorentz transformation by c/1.25 = 0.8 c. The eye which is stationary would see the collision time = L/c and the observer in the spaceship would see this L' x 1.25/c . When we multiply with the gamma factor we got a wrong equality. We solved the problem from a different way but what i could not catch is why the equation did not hold ? I started to think maybe the wrong part is that we write c in Lorentz transformation maybe this is the mistake but i could not find any clues that strongly supported my idea. Thanks you !

 

[Orodruin]

I’m sorry, but your post is difficult to parse. It is not clear to me exactly what it is you are asking and exactly what you are finding difficult or paradoxical.

 

[Ibix]

I think what you have is a frame in which the ships are each moving at 0.5c in opposite directions. The experiment starts when the ships are $L$ apart in this frame and you determine the time to collision. Then you transform to the rest frame of one of the ships and try to determine the time to collision from the start of the experiment as measured in this frame. Is that correct?

In that case, did you think about where the moving ship is at the same time as the stationary ship thinks the experiment starts?

 

[DrClaude]

Please post this in a homework forum, filling out the template.

Thread closed.