Two Balls Colliding. Check my work please

AI Thread Summary
The discussion focuses on the physics of two balls colliding, analyzing their motion using equations of projectile motion. The key points include deriving the time to reach the highest point, equating the vertical and horizontal components of motion, and finding relationships between initial velocities and angles. The calculations lead to the conclusion that the optimal angle for minimizing the expression involves using 45 degrees, resulting in a specific velocity formula. The final assertion is that when the angle is 45 degrees, the velocity simplifies to a function of distance and gravitational acceleration. The mathematical reasoning appears sound and confirms the findings.
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[PLAIN]http://img178.imageshack.us/img178/4781/345b.jpg

So I said v=v0-gt, and at the highest point, v=0, so t=v0/g.
I also said uy=u0sinx-gt, and ux=u0cosx.
So at t=v0/g, both balls have to be at their highest pint, and when uy=0, t=u0sinx/g...so equating the two times, I find u0sinx=v0...which I guess is obvious without calculation.
So uy0=v0, and ux0=v0cotx, and u0=v0/sinx.
In this time, the left ball must travel d, so ux0*t=v0cotx*v0/g=v02cotx/g=d...
I did some rearranging and found that v0=(d*g*tanx)1/2.
Since u0=v0/sinx=(d*g*tanx)1/2/sinx, we need to minimize (tanx)1/2/sinx= (1/(sinxcosx))1/2...which is a minimum at x=45o, and when x=45o, v=(d*g)1/2.
Is this right?
 
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Looks right to me.
 

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