Conservation of momentum.     m1 * v1 = m2 * v2     Mass of the projectile times speed of the projectile before impact = mass of the pendulum times speed of pendulum+projectile after impact. The ballistic pendulum was invented in 1742 by English mathematician Benjamin Robins. Sandbags have been used as pendulums for bullets. This was the first way to find out how fast a bullet was going.

The part of the video most pertinent to this experiment is from time marker 1:00 minute to time marker 3:00 minutes. The rest of the video shows an example of why conservation of momentum is relevant.

You can use a projectile as small as the airsoft pellet in the video, and a thimble for a pendulum, or you can use the guns detailed in my instructables "MONKEY HUNTER PHYSICS" and "MONKEY HUNTER PHYSICS EASIER GUN"  These of course, being larger projectiles will need a larger, heavier pendulum. 

1) weigh your projectile and pendulum. 

2) shoot projectile at pendulum

3)measure how high the pendulum + projectile swing.

4) calculate velocity of the pendulum using the formula  
Where v=velocity of pendulum,  G=acceleration of Gravity,  X= distance fallen (or in this case distance risen before it stops)

5) Calculate velocity of projectile using mV=Mv
Where m= small mass of projectile, V=big Velocity of projectile,  M=big Mass of pendulum,  and v= small velocity of pendulum.

6)If you have access to an electronic chronograph, you may want to compare results between the pendulum and the chronograph. Some pelletgun manufacturers also publish their muzzle velocities. Compare your results to published specs.