A small block of wood of inertia mb is released from rest a distance h above the ground, directly above your head. you decide to shoot it with your pellet gun, which fires a pellet of inertia mp. after the block has fallen a distance d, the pellet hits it and becomes embedded in it, kicking it upward. at the instant of impact, the pellet is moving at speed vp.
Since I'm assuming that its perfectly elastic, considering there's not enough information given, so I think that no energy is dissipated in the collision
hmax = h - d + { [ mpvp - mb√(2gd) ] / (mp+mb) }² / (2g)
