A bullet of mass m is fired vertically from below into a thin horizontal sheet of plywood of mass M that is initially at

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A bullet of mass m is fired vertically from below into a thin
horizontal sheet of plywood of mass M that is initially at rest,
supported by a thin sheet of paper (Figure 8-48). The bullet
punches through the plywood, which rises to a height, H, above the
paper before falling back down. The bullet continues rising to a
height, h, above the paper. (a) Express the upward velocity of the
bullet and the plywood immediately after the bullet exits the
plywood in terms of h and H. (b) What is the speed of the bullet?
(c) What is the mechanical energy of the system before and after
the inelastic collision? (d) How much mechanical energy is
dissipated during the collision?