The ballistic pendulum used to be a common tool for the determination of the muzzle veloci...

The ballistic pendulum used to be a common tool for the determination of the muzzle velocity of bullets as a measure of the performance of firearms and ammunition (nowadays, the ballistic pendulum has been replaced by the ballistic chronograph, an electronic device). The ballistic pendulum is a simple pendulum that allows one to record the maximum swing angle of the pendulum arm caused by the firing of a bullet into the pendulum bob.

Figure P5.41

Letting L be the length of the pendulum’s arm (whose mass is assumed to be negligible), mA be the bob’s mass, and mB be the mass of the bullet, and assuming that the pendulum is at rest when the weapon is fired, derive the formula that relates the pendulum’s maximum swing angle to the impact velocity of the bullet.