# Velocity Lorentz Transformation

1. Sep 13, 2014

### teaJ

Not sure if Velocity Addition belongs in introductory Physics but it seems relatively introductory to me. I'm having trouble with all aspects of grasping how to attempt these problems logically. Obviously the math behind them is super simple; I just more or less don't know what to plug in where.
Here's an example problem and I want to see if my logic checks out. It's not actual homework but it works all the same

1. The problem statement, all variables and given/known data
An electron whose speed to an observer in a fixed frame is .8c is being studied by a second observer in a frame moving in the same direction as the electron at a speed of .5c relative to the first observer. What is the velocity of the electron relative to the second observer?

2. Relevant equations
$v=\frac{(v_1+v_2)}{(1+v_1*v_2)}$
(obviously v1 and v2 are divided by c^2, but I left it out because it cancels and I'm not super great at typing these equations.
$v_2=\frac{(v-v_1)}{(1-v_1*v)}$
3. The attempt at a solution

So my attempt at the logic behind these problems is that you use the velocity addition when v1 and v2 have SEPARATE observers. You use the subtraction form of the equation when v1 and v2 have separate observers, so for example people on Earth observe a spaceship traveling at .5c who observes a second rocket traveling at .7c and you want to know what the speed of the second rocket is relative to the observers on Earth.

In my problem though there are two separate observers observing the same electron, one stationary in a fixed frame (K), and another in a moving frame (K'?). Since we have two observers I'm assuming that we use the subtraction form of the equation? Where V is the speed of the electron relative to the stationary observer (.8) and V1 is the speed of the moving observer relative to the stationary observer(.5)?

Can someone please explain my flaw in logic and possibly give me an easy way to figure out these problems? I'm fairly certain that my solution is incorrect. I have no real way to check, but it just doesn't feel right. I'm not confident in these problems at all. In fact I would MUCH rather do E&M problems that are much harder conceptually as well as mathematically and I know that that shouldn't be the case.

2. Sep 13, 2014

### composyte

Both of those equations are correct however, one applies for finding the electrons velocity relative to a stationary frame (K) where the other applies for a moving frame (K'). In this problem, you are trying to find the relative velocity of the electron with respect to the moving observer, which you have denoted as V2...The rest of the values, V1 and V, are both given in the problem. So finding V2 is only a matter of plugging in the values. I'm not so sure where your trouble lies, are you having difficulty with the logic behind the equations??

3. Sep 13, 2014

### teaJ

More or less yes. I think I'm over complicating the problems. I'm going to practice a few problems and see how things go. Thanks for the help.