# Relativistic velocities

1. May 8, 2013

### ZanyCat

I do have a specific example/problem, but my actual question is moreso conceptual (I'm sure that seeing someone confused by relativity is a first around here!).

The problem:

Two rockets are each 1000m long in their rest frame. Rocket Orion, traveling at 0.900c relative to the earth, is overtaking rocket Sirius, which is poking along at a mere 0.700c. According to the crew on Sirius, how long does Orion take to completely pass?
That is, how long is it from the instant the nose of Orion is at the tail of Sirius until the tail of Orion is at the nose of Sirius?

_____________________________________________________________________________________

Okay, so I'm thinking that I'll need to find a) the observed velocity of O in S's FOR and b) the observed length of O in S's FOR, and go from there.

My confusion is coming from the velocities. I'm taking S as my Frame of Reference, so from S's FOR, is O moving past at 0.200c? Or do I need to transform the velocity?

2. May 8, 2013

### Staff: Mentor

Good.

No. To find the velocity of O with respect to S, you'll need to use the relativistic addition of velocity formula.

3. May 8, 2013

### ZanyCat

I'm struggling with that part. Do I need to consider the earth as my stationary FOR, then?

4. May 8, 2013

### ZanyCat

Never mind, got it sorted, thanks Doc!