[JesseK]

Assuming a 60 degree arc length of contact on a 8" 1-wheel shooter at ~2400 RPM, the ball needs a minimum of 500 watts transferred to it after inefficiencies in order to go 54 feet (~42 ft/s for middle goal). This is doable with a heavy flywheel that has plenty of spin-up time and 4 Banebots RS-550 motors connected to the same wheel. At 63% overall efficiency, that's ~67 amps of current while a ball is in the shooter. If you sit in one spot, that's chump change.

The kinematic equations are your friends this year.
Vf^2 = Vi^2 + 2 * a * d
You have D, Vf, and Vi. You can find a, which then can give you required force via F = m * a, and then a torque via Tau = Force * radius of the wheel. Then you can multiply Torque (N*m) * Wheel speed (rotations / second) and you get power required.

Of course, that assumes a perfect flywheel effect and a perfect contact patch between ball and wheel, so YMMV. Prototype it.

It also assumes that a 84" tall robot will never block the shot, heh. We aren't even attempting it because the trajectory length is so long that a variance of ~0.7 degrees in the shooter causes the shot to miss. That's not worth putting 4 motors on the shooter.