# Coming to terms with the velocity addition formula

1. Aug 10, 2008

I have two rockets, one in point A and another in point B, I'm going to crash one against the other, twice, and I will be observing safely from my laboratory at C, which is right in the middle between A and B.

The first time the experiment takes place, I see both rockets rushing forward to one another at a constant speed of 0.75c, they meet and crash right in the middle point between A and B.

The second time, the rocket at A is at rest relative to me, and I see the other rocket moving towards it from B at a speed of 0.96c, they meet and crash at A.

Using the velocity addition formula to calculate what the speed of B relative to A was in both experiments, we'd get precisely 0.96c, which I believe means that for the rocket at A, both experiments should produce the exact same results (let's define results as the amount of damage in the ships), which means that both experiments should produce the exact same results in every reference frame.

I'm just having trouble digesting this from the reference frame of the laboratory, where the configuration of each of the two experiments seems somewhat different as to produce the exact same results. In the first experiment, considering the laboratory frame exclusively, after one meter of time has passed, the rockets are 1.5 meters closer than they were before, whereas in the second experiment, after one meter of time has gone by, they're only 0.96 meters closer to each other.

I think I'm just trying to find a way to visualize these results without having to analyze the experiments from the reference frame of either of the ships.

2. Aug 10, 2008

### DaveC426913

Have you accounted for
1] time contraction when measuring simultaniety of events?
2] length contraction of the rockets?
When you do, you should find the discrepancy evaporates.