[dsirovica]

Mathematacally this is hard to compute - but you don't need to.

For the purposes of this game the key issue is repeatability of the shot. So you can calibrate the system to hit the "kill zone" and as long as it is repeatable - who cares about the math (again for the purpose of this game).
However you wil need to place your robot at the same place and orientation every time. Or a set of predefined positions.

Repeatability is tricky though, because you need to place minimization of errors as a key design rule for all you do. We hear for example that the weight of the balls is within a 10% range. When faced with an item that has such an inbuilt error, one needs to design mechanisms that reduce the significance of that error on the outcome.That is indeed what design engeneers do all the time, and there are multiple ways of doing it.

Good discussion,
Dean