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So I said v=v_{0}-gt, and at the highest point, v=0, so t=v_{0}/g.

I also said u_{y}=u_{0}sinx-gt, and u_{x}=u_{0}cosx.

So at t=v_{0}/g, both balls have to be at their highest pint, and when u_{y}=0, t=u_{0}sinx/g...so equating the two times, I find u_{0}sinx=v_{0}...which I guess is obvious without calculation.

So u_{y0}=v_{0}, and u_{x0}=v_{0}cotx, and u_{0}=v_{0}/sinx.

In this time, the left ball must travel d, so u_{x0}*t=v_{0}cotx*v_{0}/g=v_{0}^{2}cotx/g=d...

I did some rearranging and found that v_{0}=(d*g*tanx)^{1/2}.

Since u_{0}=v_{0}/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?

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# Homework Help: Two Balls Colliding. Check my work please!

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