If I could link you over to my post of ether's trajectory calculator with my additions to the base framework of it all, I gave perspective to the field as to where you would be shooting from and the distance as well as ideal shooter values
http://www.chiefdelphi.com/media/papers/3217
The base equations didn't change however I put in a few approximate values of upper and lower gates where the boulder this year would go into the goal. the range finder has lines placed on the field for where the boulder would need to shoot from to get into the goal. if you work out the direct output from your mechanism to the ball for speed you could also then adjust the rpm for launch velocity. at the peak time on the sheet the Velocity in the Y direction should be equal to 0 and would allow for you to get the ball into the goal.
I would recommend as high of an entrance point into the goal so that if there are variations in power or rpm the boulder will still pass the plane of the goal.