The shot is a parabola
only if you neglect air resistance.
Does anyone have a good number for the terminal velocity of this year's ball? If so, you can use
this trajectory calculator (ignore the green lines).
If you want to hit the goal at the trajectory's apex at different distances from the goal, you can't pick one wheel speed and use it for all shots. For a given desired distance to and height of the apex, there is a unique launch angle and launch speed solution.
Shooter consistency is going to be your number one challenge. Consistency will be affected by:
- errors in measurement of distance to goal
- errors in setting and maintaining a wheel speed
- errors in setting a launch angle
- variations in ball weight, size, compressibility, elasticity, and surface texture
If you can solve the above problems, then using a lookup table is likely the most straightforward and accurate approach.
Experimentally determine the proper angle and wheel speed for each distance from the target and put it in the table.
You have a big challenge ahead of you. I hope you are successful.