A pendulum with a mass of 1kg. on a light string 1 meter long is dropped from a position with the string held level falling until it as its lowest point. At that instant it is struck by a bullet moving in precisely the opposite direction. The bullet has a mass of 50 grams, and it is noted that the two objects which stick together continue in the direction of the pendulum's motion but rise only half as high as the starting point.
a) What is the velocity of the bullet?
b) How much energy is lost (converted to non mechanical form) during the collision?