The simplest way of making a rough estimate would be to consider the problem from an energy conservation perspective.
The increase in potential energy of your pendulum should be equal the decrease in kinetic energy of the projectile:
dEkin + dEpot = 0
This is pretty rough since some energy will be expended deforming your projectile, localised heating, wind resistance, non-perfect wires, etc.
dEpot = (m+M)*g*dh - where
m is the mass of the projectile,
M the mass of the pendulum,
g the gravitational constant and
dh the change in height of the pendulum.
dh = l * cos(theta) - where
l is the length of the wire and
theta is the deflection angle.
The velocity should then be given by:
v = sqrt(2*(m+M)*g*l*cos(theta)/m)
It's important that you choose the weight of the pendulum carefully in relation to the weight of the projectile. It is also important that the entire projectile moves with pendulum. You need to establish the centre of mass of the pendulum fairly precisely - or use a very long wire.
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