A physical pendulum consists of a vertical board of of mass 6.12 kg, length 191 cm, and width 12 cm hanging from a horizontal, frictionless axle. A bullet of mass 143 g and a purely horizontal speed v impacts the pendulum at the bottom edge of the board. The board then makes a complete circle.

(a) If the bullet passed through the board, reducing its speed by a factor of 1/3, what is the minimum speed of the bullet?
(b) If the bullet embedded itself in the board, what is the minimum speed of the bullet?

Note (hint from instructor): It appears you may use Conservation of Energy to find angular speed. For potential energy: use center of mass. For kinetic energy, use impulse. Then, to find initial speed, use conservation of angular momentum.