A bullet of mass m is fired vertically from below into a block of wood of mass M that is initially at rest, supported by a thin sheet of paper. The bullet blasts through the block, which rises to a height of H above its initial position before falling back down. The bullet continues rising to height h.

(a) Express the upward velocity of the bullet and the block immediately after the bullet exits the block in terms of h and H.

(b) Use conservation of momentum to express the speed of the bullet before it enters the block of wood in terms of given parameters.

(c) Obtain expressions for the mechanical energies of the system before and after the inelastic collision.

(d) Express the energy dissipated in the block of wood in terms of m, h, M, and H.