Two Balls Colliding. Check my work please

[mmmboh]

[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 u_y=u₀sinx-gt, and u_x=u₀cosx.
So at t=v₀/g, both balls have to be at their highest pint, and when u_y=0, t=u₀sinx/g...so equating the two times, I find u₀sinx=v₀...which I guess is obvious without calculation.
So u_y0=v₀, and u_x0=v₀cotx, and u₀=v₀/sinx.
In this time, the left ball must travel d, so u_x0*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=45^o, and when x=45^o, v=(d*g)^1/2.
Is this right?

 

[kuruman]

Looks right to me.