Special relativity transformations

[zhillyz]

Homework Statement

Two light flashes occur on the laboratory x axis, the first at time t=0 and
position x=450 m, the second at time t=+1 ms, at the origin. In an inertial
frame moving along the x-axis with speed v, the events are simultaneous.
What is the speed v?

Homework Equations

From the question I have decided that the relevant equations are the Lorentz transformations. We know the position's in the rest frame and we know the time of the events. In the moving frame we know the the events are simultaneous. So we can't use the transforms for x as there would be two unknowns [itex]\Delta x'[/itex]and [itex]v[/itex]

The Attempt at a Solution

[itex] t_{1}' = \gamma (t_{1} - \dfrac{vx_{1}}{c^2})[/itex]
[itex] t_{2}' = \gamma (t_{2} - \dfrac{vx_{2}}{c^2})[/itex]

[itex] t_{2-1}' = \gamma (t_{2} -t_{1} - \dfrac{v}{c^2}(x_{2} - x_{1}))[/itex]

[itex] 0 = \gamma((1*10^-3) - 450\dfrac{v}{c^2})[/itex]

[itex] 0 =(1*10^-3) \gamma - \gamma 450\dfrac{v}{c^2}[/itex]

[itex] \gamma 450\dfrac{v}{c^2} =(1*10^-3) \gamma [/itex]

[itex] 450\dfrac{v}{c^2} = (1*10^-3) [/itex]

[itex] v = \dfrac{(1*10^-3)}{450} c^2 \mbox{WRONG!}[/itex]

Not sure what I am doing wrong. Any help on how to tackle these questions would be great.

 

[zhillyz]

Unless question sheet is a misprint and it should be micro rather than milli(seconds)?

 

[fishistheice]

Your reasoning seems to be correct, and using the numbers given does give a non-physical result, so you are perhaps correct in thinking that there is a misprint in the question.

 

[zhillyz]

Thanks, my lecturer got back to me and confirmed this :). I appreciate you taking the time.

 

[Nickie]

It seems like you are on the right track by using the Lorentz transformations, but there are a few mistakes in your calculation. First, you have used the wrong value for t1 in your first equation. It should be t1 = 0, since the first event occurs at t=0 in the rest frame. Second, you have used the wrong value for t2 in your second equation. It should be t2 = 1 ms, since the second event occurs at t = +1 ms in the rest frame. Third, you have used the wrong value for x2 in your last equation. It should be x2 = 0, since the second event occurs at the origin in the rest frame.

Also, keep in mind that the Lorentz transformations involve the speed of light, c, not c^2. So the correct equation should be 450v/c = 1*10^-3. Solving for v gives you v = 2.22*10^6 m/s.

Hope this helps! Remember to always double check your inputs and units when using equations in physics.