The inexperienced hunter aims his gun directly at the monkey, rather than correcting for gravity. However, the monkey lets go of the branch at the exact instant that the gun fires. The result is that the bullet strikes the monkey.
Make sure you blow on the tube hard enough that the ball bearing hits the monkey before it hits the ground. Also, don't forget to wear your pith helmet.
There's a possibly useful transparency that can be used with the demo to help explain the motion.