Momentum:

$\overline{){\mathbf{p}}{\mathbf{=}}{\mathbf{m}}{\mathbf{v}}}$

Kinetic energy:

$\overline{){\mathbf{K}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{m}}{{\mathbf{v}}}^{{\mathbf{2}}}}$

Gravitational potential energy:

$\overline{){\mathbf{U}}{\mathbf{=}}{\mathbf{m}}{\mathbf{g}}{\mathbf{h}}}$

Pendulum SHM equations:

In a ballistic pendulum an object of mass *m* is fired with an initial speed *v*_{0} at a pendulum bob. The bob has a mass *M*, which is suspended by a rod of length *L* and negligible mass. After the collision, the pendulum and object stick together and swing to a maximum angular displacement θ as shown (Figure 1)

**Find an expression for v0, the initial speed of the fired object.**

Express your answer in terms of some or all of the variables *m*, *M*, *L*, θ and the acceleration due to gravity, *g*.

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