# Relativistic composition law for velocities

1. Oct 27, 2009

### 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?

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

3. The attempt at a solution
So I think I know a and b, but thats 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.

2. Oct 28, 2009

### tiny-tim

Hi maxwilli06!

(try using the X2 tag just above the Reply box )
No, you should be getting 2v/(1 + v2/c2)