The ballistic pendulum is a device used to measure the speed of a bullet. A bullet of mass m is fired into a block of mass M hanging on a pendulum of length L, into which it embeds itself; this causes the pendulum to swing up to some maximum angle 0, as shown. Calculate the initial speed of the bullet in terms of m, M, 0, L, and g. (Hints: What conservation laws might you be able to apply in this problem? When can you apply each one, and when can you not?) L m M
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