What Happens in Vegas...

...stays in Vegas.

Similarly, what happens on the x-axis stays on the x-axis. The same goes for the y-axis. This can be summed up in the sentence, "Axes are independent."

So what does this mean?

They function without each other; the velocity on the x-axis does not affect the velocity on the y-axis.  This can be proven  in the very simple example we saw and heard in class involving two pens. Both pens were released from the same height. The difference is that one pen was just dropped while the other was projected horizontally. Both pens landed at the same time, which proves that the axes are independent of each other.