One way of measuring a projectile's speed is by using a ballistic pendulum, as shown below.
This pendulum is a piece of wood of mass , suspended by a fine, lightweight wire. Initially, the pendulum is at rest. A bullet of mass horizontally strikes the piece of wood and gets stuck in it, causing the pendulum to lift up at height .
If the mass of the pendulum is , the bullet's mass is , and after impact they lift up to , what is the initial speed (in ) of the bullet (to the nearest integer)?
Details and Assumptions: