Question

A 5 gram bullet is fired into a 7 kg ballistic pendulum suspended vertically from the ceiling. If the bullet embeds into the block and the two move as one to a new final height of 12 cm. What was the initial velocity of the bullet before impacting the pendulum?

Answer 1

The moment when the bullet collides with the block, is the max of kinetic energy of the system (bullet embeds block). When the system swings to the maximum height = 12cm, it's when kinetic energy converts to potential energy. So that, Max-of-kinetic-energy = Max-of-potential-energy
=> 0.5*(m+M)*V^2 = (m+M)*g*h
=> V = sqr(2gh)

Apply the rule of conservation of momentum, we have:
m*v + M*0 = (m+M)*V
=> v = [(m+M)*V]/m