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w3390
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Homework Statement
A rocket with that has a proper length of 1100 m moves away from a space station in the + x direction at 0.60c relative to an observer on the station. An astronaut stands at the rear of the rocket and fires a dart toward the front of the rocket at 0.85c relative to the rocket. How long does it take the dart to reach the front of the rocket as measured in the reference frame of the space station?
Homework Equations
u=[tex]\frac{u'+v}{1+\frac{v*u'}{c^2}}[/tex]
The Attempt at a Solution
I worked through the algebra of the above equation by assigning u to the velocity of the dart relative to the space station, u' to the velocity of the dart relative to the rocket, and v to the velocity of the rocket relative to the space station. The result was that the dart is traveling at .96c relative to the space station. Since I have found the speed of the dart in the frame of the space station, do I then have to find how much the rocket contracts and then determine the time it takes to travel or I am wrong in this line of logic? If this logic is correct, the answer I got was 3.8 microseconds by dividing the proper length of the rocket by the velocity of the dart.
Thanks for any help.