Molecular dynamics simulations demonstrate facile dissociation of halogen molecules embedded in rare gas clusters upon impact at a surface at collision velocities up to 10 km/s. Two pathways are discerned: a heterogeneous dissociation of the molecule on the surface and a homogeneous mechanism where rare gas atoms which have rebounded from the surface cause the translational-vibrational coupling. The total yield of dissociation of the clustered molecule can reach up to 100%, whereas the yield of dissociation of the bare, vibrationally cold molecule saturates below 40%. A systematic study of the role of different conditions is made possible by not accounting for the atomic structure of the surface. The role of dissipation at the surface is found, however, to be quite important and is allowed for. Larger clusters, clusters of the heavier rare gases and a more rigid surface, all favor the homogeneous mechanism. Evidence for a shock front which, upon the initial impact, propagates into the cluster; the binary nature of the homogeneous dissociation process; and the absence of a dominant cage effect are discussed. A quantitative functional form of the velocity dependence of the yield of dissociation, which accounts for the size of the cluster, the rigidity of the surface and other attributes, is used to represent the data. The physics of the processes within the cluster is dominated by the novel dynamical features made possible when the duration of the atom - molecule collisions is short compared to the vibrational period. This "sudden" regime is sudden with respect to all modes of the nuclear motion and provides a hitherto unavailable tool for examination of reaction dynamics under extreme conditions.