Relativistic composition law for velocities

[maxwilli06]

I'm in desperate need of some help. I am so lost on this:

1. imagine a rocket ship R moving eastward with speed v with respect to the Earth and a rocket ship S moving westward with speed −v with respect to the earth, we wish to know the speed of R with respect to S.

a. Go to a reference frame moving with S. How fast and in what direction is the Earth
moving in that reference frame?

b. How fast and in what direction is R moving with respect to the earth?

c. Using the equation for composition of velocities calculate how fast R is moving with
respect to S. Let x = v/c and y = w/c. Calculate y (x) for 5 values of x between 0
and 1 and make a rough graph of the function in that interval.

d. How does w depend on v for v << c ? What law does this illustrate?

e. How does w depend on v for v → c ? What law does this illustrate?

Homework Equations

The relativistic composition law for velocities is
w = (u + v) /( 1 + uv/c^2)

The Attempt at a Solution

So I think I know a and b, but that's about it.

a) In the reference frame with S, the Earth is moving west at velocity v.
b) In the reference frame of earth, R is moving east at velocity v. In R’s frame of reference, Earth is moving west at velocity v (value of –v on a graph.)
c) I always only get 1 for this equation. If you take R and S, and their velocities, I get 0 for the first bit of the equation so it has to be one? I'm really messing up hear and the rest of the problem requires me to get this right.

 

[tiny-tim]

Hi maxwilli06!

(try using the X² tag just above the Reply box )

If you take R and S, and their velocities, I get 0 for the first bit of the equation …

No, you should be getting 2v/(1 + v²/c²)