In the bit I quoted, you said "for the first ball from the top, it's velocity is 2m/s" which I took to meaning its velocity when it left the top.
However, it now seems we're happy with the following:
Uniform acceleration, a = -1 m/s^2 (note the negative if we're defining up from the bottom of the ramp to the top)
Ball 1 initial position x1,0 = 8 m
Ball 2 initial position x2,0 = 0 m
Ball 1 initial velocity u1 = 0 m/s
Ball 2 initial velocity u2 = ? m/s
Ball 1 velocity at impact = ? m/s
Ball 2 velocity at impact = 0 m/2
Ball 1 position at impact = Ball 2 position at impact = x = ? m/2
Time at impact t = ? s
So now you can write out the equations of motion for both balls, and work out which ones are relevant. However, it looks like you've already done that but made a significant mistake.
Sepens wrote:Oh, I also know that the first ball's distance down the ramp can be measured by .5t^2, but that isn't too helpful as of yet.
Are you using s = ut + 1/2 at^2? I suspect you are, so there are a couple of problems with that. Firstly, as I mention above, you need to make sure you treat up/down and positive/negative values consistently, otherwise you'll wind up with strange results like objects flying out into space. Secondly, that equation only holds for motion that starts at the origin. Look at the information you have - with no collision, at 0s the ball is at 8m, and at 4s the ball is at 0m. Does that fit your equation? Can you adjust your equation to make it work? Because if so, you should be several steps closer to solving your problem.