You can use either banner sensors with reflective tape or the photoswitches from this year's kit to do it in code. Put them across the exit point of your shooting mechanism.
Start a timer when the interrupt from the beam being broken occurs, get its value when it sees the other side again, and do some math (since the ball is 7" in diameter).
If a ball is going 12m/s, it will take about 14.8ms between these events, well within the capabilities of the RC's timer resolution (see
www.kevin.org/frc for how to use timers).