What is the missle's speed with respect to the planet?

[*64]

i am working though some practice Q's in my course book and i am stuck on this question, the book doesn't give fully worked answers so I am not sure if this is correct or not

a spacecraft moving at 0.75c fires a missle travlling at 0.30c with respect to itself at a stationary planet, what is the missles speed with respect to the planet

i think i need to use

u = v1+v2 / 1 + v1xv2 / c^2

but i am not sure if this is going to give me the speed with respect to the planet, i think i need a bit more help with how to set up the inertial frames

the frame of the spaceship is S then the missle is S' and the planet S'' ?

thanks

 

[Doc Al]

I find it useful to write the Relativistic addition of velocities like this:

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

Where V_a/c means the velocity of a with respect to c. In your problem, let a stand for the missle, b for the rocket, and c for the earth.