Calculate the bullet speed

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 \(M\), suspended by a fine, lightweight wire. Initially, the pendulum is at rest. A bullet of mass \(m\) horizontally strikes the piece of wood and gets stuck in it, causing the pendulum to lift up at height \(h\).

If the mass of the pendulum is \(M=4\text{ kg}\), the bullet's mass is \(m=9.7 \text{ g}\), and after impact they lift up to \(h=19\text{ cm}\), what is the initial speed (in \(\text{m/s}\)) of the bullet (to the nearest integer)?

Details and Assumptions:

  • The gravitational acceleration is \(g=9.8\text{ m/s}^2\).

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