I thought of this at 2:00 AM when I couldn't sleep.

OK, before I start, you need to know my syntax for velocity.
V"object"("Reference")

Now, we have three objects in the system X, Y, and Z.
Objects X and Y are going to either colide head on or are travelling in opposite directions.
if VX(Z)>=C/2 and VY(Z)>=C/2 then VX(Y)>=C and VY(X)>=C. Right?

Since you can't measure velocity without a reference point, you can change the velocity of an object by changing the reference point.

Is there something I am forgetting?

You can indeed change the measured velocity of an object by changing your reference frame. The problem with what you've done here is the assumption that velocities transform in a linear way between different frames. This holds to a very high degree of accuracy for small velocities. For velocities closer to the speed of light, this assumption doesn't hold. The equations needed to convert velocities between different reference points then are the Lorentz Transformations (http://en.wikipedia.org/wiki/Lorentz_transformation#Matrix_form).

I went to a public school. Can you get me from intro trig to what is required there?

I would recommend starting with the derivation of the Lorentz factor here:

http://en.wikipedia.org/wiki/Time_dilation (under the section "Simple inference of time dilation")

Now heres a nice simple derivation of the relativistic velocity addition rule using only algebra and the Lorentz factor:
http://tinyurl.com/5chh83

The formula is usually derived with the Lorentz transformations, but those can be a bit more difficult to derive.

The Lorentz Transformations can be derived using only basic algebra. As a starting point, consider a flash of light, originating from a point, viewed from two different reference frames. The light wave must be spherical and expand with velocity c in both frames. Can you figure out where to go from here?

Yes, I have to go inside the building and up a flight of stairs.

No, can someone just tell me how to implement Lorentz Transformations in my scenario?



I am more of a conceptual thinker. Like Einstein and his cows.

I thought of this at 2:00 AM when I couldn't sleep.

OK, before I start, you need to know my syntax for velocity.
V"object"("Reference")

Now, we have three objects in the system X, Y, and Z.
Objects X and Y are going to either colide head on or are travelling in opposite directions.
if VX(Z)>=C/2 and VY(Z)>=C/2 then VX(Y)>=C and VY(X)>=C. Right?

Since you can't measure velocity without a reference point, you can change the velocity of an object by changing the reference point.

Is there something I am forgetting?

Your question is confusing. Where are x,y and z?

x---y----z

Like that in a line?

You can't add velocities the normal way in relativity: http://en.wikipedia.org/wiki/Velocity-addition_formula

X->.................... <- y
.............. Z
or

<-X... Y->
..... Z

While Z would notice that the distance between X and Y is increasing/decreasing at a rate c in his own reference frame, this is not what X or Y would see. Rather, by the velocity addition formula (v1 + v2)/(1+v1*v2/c^2), they would see each other moving towards/away at (4/5)c.