[Rickertsen2]

well there are a few ways. If you can shoot your launcher straight and measure the height it reached then use the formula v=sqrt(2gh)

it was derived from conservation of energy
kinetic energy = (mv^2)/2
potential energy =
mgh=(mv^2)/2
2mgh=mv^2
2gh=v^2
v=sqrt(2gh)

If you can't launch straight up but can launch straight ahead and measure the distance it fires from a known height then:

v=d/(.45sqrt(h))

where h is the height between the launch point and the floor. d is the distance traveled before hitting the floor. Everything must be in SI units.