Help Understanding Lorentz Factor

[mdergance3]

If I am at rest and I observe a train moving past me at .9c and then the train fires a projectile at .5c relative to it how fast do I observe the projectile moving?

With the speeds given, the lorentz factor is 2.294. I made the incorrect assumtion that I could just take the .5c and divide it by the lorentz factor since S = d/t and time is now 2.294 times slower.

How do I find the correct observed speed?

 

[tiny-tim]

hi mdergance3!

see http://en.wikipedia.org/wiki/Addition_of_Velocities_Formula#Special_theory_of_relativity"

 

[GRDixon]

If I am at rest and I observe a train moving past me at .9c and then the train fires a projectile at .5c relative to it how fast do I observe the projectile moving?

With the speeds given, the lorentz factor is 2.294. I made the incorrect assumtion that I could just take the .5c and divide it by the lorentz factor since S = d/t and time is now 2.294 times slower.

How do I find the correct observed speed?

Apply the velocity transformation.

 

[Matterwave]

For this the simplest way is to just use the velocity addition formulas. If you want to know where that formula came from, though, you can do 2 lorentz boosts, one from the projectile's Frame to the train frame, and then from the train frame to the platform frame.