impulse and momentum:ballistic method ?

Question

A 20 gram bullet is fired horizontally into a 5 kg block of wood suspended by a long cord. The bullet sticks in the block. Determine the velocity of the bullet if the inelastic collision causes the block to swing 0.08m above its intial level.

Answer 1

You need to use conservation of energy to determine the initial velocity of the block and bullet complex, which can be done because the initial kinetic energy will be equal to the gravitational potential energy at the top of the swing. Then you use conservation of momentum to calculate the initial velocity of the bullet that corresponds to the velocity of the block and bullet complex as calculated immediately before.

Say that the bullet has a mass of m and the block has a mass of M, and the swing height is h; all of these values have been given. First use conservation of energy to show that KE_initial = GPE_final ==>0.5*(m+M)v^2 = (m+M)gh, and solve algebraically for v. Then conservation of momentum shows that mV = (m+M)v, where V is the velocity of the bullet and can be solved for algebraically.