Our kicker is based on pendulum theory.
But we didn't calculate the force to kick the ball.
We worked with Angle(A) between Kicker and Ball and Tangencial Velocity(Vt) of the Pendulum.
So we used the follows equations:
Ymax (Maximum Height): (Vt*sen(A))²/2g
Xmax (Maximum Distance): (Vt²*sen(2A))/g
You'll find your maximum distance and maximum height based in Angle and Tangencial Velocity.
PS: If you wanna know the "perfect" kick (no considerations of air drag), in order that the ball doesn't hit in your bumper and pass trough 2 BUMPS, you'll need find the coeficients
a and
b of the equation F(x)=ax²+bx+c (the coeficient
c you don't need to find because your parable doesn't cross the Y axis.
Man, I really don't know if you could understand what I'm thinking about, because I never had discussed math or physics in english language, but this method worked for our team:
http://www.youtube.com/watch?v=QMqMi_OIuRY
We vary the angle between the tests, and, as you can see, the ball pass trough Bumper and both bumps without hit in the bumper!