Chapter 11, Problem 72PQ

A pendulum consists of a wooden bob of mass M suspended by a massless rod of length ℓ. A bullet of mass $m\ll M$ is fired horizontally with speed v at the bob and emerges from the bob with speed v/3 as shown in Figure P11.72. If the pendulum bob just barely reaches the highest point such that it is able to swing through one complete circle, find an expression for the speed v of the bullet before the collision.

FIGURE P11.72