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I am a bit confused about the length contraction formula. The formula is :

l=lo*sqrt(1-u^2/c^2), where lo is the distance measured in a frame at rest with the moving object.

Now I was looking at a problem where a spacecraft just as it touches the finish line (event 1) a message from the back (which is measured by the astronaut to be 300m) is simultaneously sent (event 2).

Now, using Lorentz trans. an observer standing just at the finish line will say that event 2 occurred at x=375m.

My confusion.

I would like to consider the spacecraft as a whole, as a single object with the front just at the finish line and the back where event 2 occurred. In that case, the astronaut will say the length of the space craft is 300m. By definition of proper length that should be the proper length because it is being measured by the astronaut who is at rest with the craft.

So if I plug that into the formula for length contraction I should expect the result to be shorter as measured by the observer standing at the finish line. That is x should be less than 300m.

I know I am wrong somewhere in my thinking and I hope someone will point that out.

Thanks.

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# Confused about length contraction

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