Astrotrain, a Decepicon triple changer, is traveling at a speed of .77c towards Earth, as seen by Blaster, who is on Earth inside Fortress Maximus. Astrotrain's computers tell him the icon rocket was fired at .35c. Determine the length of the ion rocket as seen by Blaster and Fortress Maximus.
3 answers
Um, how can one determine a relativistically affected length, if no length at all is given in the problem?
I apoligize. I forgot to include that Astrotrain fired a 3m ion rocket at Fotress Maximus.
The speed of the rocket relative to Earth must first be computed. There is a relavistic velocity-addition formula for that. You can find it at
http://en.wikipedia.org/wiki/Velocity-addition_formula
The value for the relative velocity is
v = (.77c + 0.35c)/[1 + (0.77*0.35)]
= 0.882 c
Now use the Fitz-Gerald contraction formula for the apparent length of the rocket, L', as seen from Earth
L' = L * sqrt[1 - (v/c)^2]= 0.471 L
= 1.41 m
http://en.wikipedia.org/wiki/Velocity-addition_formula
The value for the relative velocity is
v = (.77c + 0.35c)/[1 + (0.77*0.35)]
= 0.882 c
Now use the Fitz-Gerald contraction formula for the apparent length of the rocket, L', as seen from Earth
L' = L * sqrt[1 - (v/c)^2]= 0.471 L
= 1.41 m
1 answer