[SenorZ]

Ball diameter ~ 8"
Hoop diameter ~18"
That is some serious leeway for close shots, but a little tighter percentage-wise for shots from the top of the key and beyond.

What I would do, and will attempt to for my kids, is implement the solution to this set of equations:

y = height difference from launcher to hoop
x = horizontal distance from launcher to hoop center
a = angle above horizontal for launcher
t = time in air
g = accel of gravity

y = v*sin(a) - 0.5g*t^2
x = v*cos(a)*t

If you know y, and g, you can substitute and solve to eliminate t. Then the two variables are x and a. The analytic solution is, well, ugly, and you'll need a computer to assist, but if you enter values it is a bit easier.