Special Relativity of rocket relative to you

[tombarrtt]

Homework Statement

Studying Special Relativity at the moment, and having a little trouble getting to grips with it. I've got stuck on this question, and was wondering if anyone could clear it up for me?

Here's the question:

"A rocket is traveling at 0.6c, v, along the x-axis relative to you. It fires a missile in the y-axis (perpendicular to the rocket in the rocket's reference frame) at 0.7c relative to you.

What speed and at what angle to the x-axis do you see the missile travelling?"

I think you have to use the Lorentz transformations for velocity, but I'm not sure.

Homework Equations

I think: ux' = (ux-v)/(1-uxv/c^2)

and: uy' = uy/(gamma*(1-uxv/c^2))

The Attempt at a Solution

I think you have to use the Lorentz transformations for velocity, but I'm not sure. I'm just getting confused with which reference frames to choose for the rocket, and what the variables "ux", "ux'" and "v" are and how to put them in.

 

[tiny-tim]

welcome to pf!

hi tombarrtt! welcome to pf!

"A rocket is traveling at 0.6c, v, along the x-axis relative to you. It fires a missile in the y-axis (perpendicular to the rocket in the rocket's reference frame) at 0.7c relative to you.

What speed and at what angle to the x-axis do you see the missile travelling?"
…
I think you have to use the Lorentz transformations for velocity, but I'm not sure. I'm just getting confused with which reference frames to choose for the rocket, and what the variables "ux", "ux'" and "v" are and how to put them in.

i think the Lorentz equations for velocity are too difficult to remember :redfae:

start with the equation of the missile in the rocket's frame …

that's x' = 0, y' = u't'

(you don't know yet what u' is, but you do know that the equivalent speed u in your frame is 0.7c)

now use the Lorentz transformation to convert that to your frame, find u, and put it equal to 0.7c …

what do you get? ​

 

[tombarrtt]

Sorry I'm just still really confused. "v" is the x-velocity of the rocket right, so 0.6c? Then what are Ux and Ux'? Is Ux' the transformed velocity into our frame? But then what is Ux, surely that's the same as v?

I'm just so confused by this :/

 

[tiny-tim]

hi tombarrtt!

solving maths problems often just involves giving everything sensible names, so that you can clearly see what you're doing

in this case, you need to differentiate clearly between the speed of the rocket and of the missile

so I'm using v for the rocket, and u for the missile ​