Relativity : Lorentz Transformation.

[Delzac]

Homework Statement

Star Trek Question: An enemy Klingon spaceship moves away from Earth at a speed of 0.80c. The Starship Enterprise gives chase and pursues at a speed of 0.90c relative to the Earth. Observers on Earth see the Starship Enterprise overtaking the enemy ship at a relative speed of 0.1c. With what speed is the Starship Enterprise overtaking the Klingon spaceship, as observed by the crew of the Enterprise?

Homework Equations

V_{a/c} = \frac{V_{a/b} + V_{b/c}}{1 + (V_{a/b} V_{b/c})/c^2}

U'_x = \frac{U_x - V}{1 - (U_x V)/c^2}

The Attempt at a Solution

I used this formula:

U'_x = \frac{U_x - V}{1 - (U_x V)/c^2}

Sub in the value where, U_x = 0.80c V = 0.90c

Then i obtained the answer, U'_x = -0.357c

Is this correct?

Also, can someone explain to me what each symbol of the 2 formula means?(the lecture wasn't very clear)

V_{a/c} = \frac{V_{a/b} + V_{b/c}}{1 + (V_{a/b} V_{b/c})/c^2}

U'_x = \frac{U_x - V}{1 - (U_x V)/c^2}

Any help will be greatly appreciated.

 

[koofle]

Your answer corresponds with mine.

And for the two equations:
The second equation listed at the end, involving U':
you have two inertial frames, let's say S, and S'. The S' frame is moving at a speed V(observers on spaceship), while frame S is motionless (observers on Earth).

lets add your Klingon spaceship

U is the velocity of the Klingon spaceship as observed in S.
V is the speed of frame S' (i.e. the speed of the Starship Enterprise)
U' is the speed of the Klingon Spaceship as observed in S'.

and c is the speed of light.The first equation you have there,
V_{a/c} = \frac{V_{a/b} + V_{b/c}}{1 + (V_{a/b} V_{b/c})/c^2}
is the velocity addition formula. Let's say you measure the velocity (V_{b/c}) of a particle in the moving S' frame, which is traveling at V_{a/b}. Then from a "fixed" frame S, the velocity (V_{a/c}) of the particle can be found using that equation.

In star trek terms:
Let S be the fixed, motionless frame of the observers on Earth, and S' be the frame of the people on board the Enterprise.
The crew on board the Enterprise see the Klingon spaceship move with a velocity V_{b/c} (which is the answer you found from the question). The Enterprise (frame S') itself is moving at a velocity V_{a/b}. Then you can use these two velocities to find the velocity of the Klingon spaceship as observed from earth, V_{a/c}.I'm learning relativity right now too, in my mechanics course, so I hope this is helpful. I wish my professor made our homework questions this interesting too.

 

[Delzac]

Ah, i see, thanks for the help.