I was going over a question on my own, then I took a brief look at the solution...it's basically about
A rocket has a proper length of 250 m and travels at a speed v = 0.950c relative to the Earth. A missile is fired from the back of the rocket at a speed u′ = 0.900c relative to the rocket. Find the time it takes observers to calculate the time it takes for the missle to move to the front of the rocket.
When I was thinking about the question, it's pretty standard.
There are two ways about this question: Method 1:
-Work out the time required for the missle to reach the front relative to the rocket (so the rocket is the frame of reference) -Apply lorentz transform and find the time observed by people on Earth)
-Find gamma -Use addition laws to find rocket's speed relative to people on earth
Here's what I don't get:
I've worked round it and realized the correct way is to use Δx = γ(Δx′ + v Δt′). Then just use distance = speed * time to work out the time (which agreed with my original answer in method 1) What I don't understand is why do we not apply length contraction to the rocket when it clearly is travelling at relativistic speeds and hence appears shorter to observers on Earth? Technically the rocket should become shorter and hence time also shorterns. Is there something I'm clearly not understanding here?