The physics of hypervelocity impacts into foams is of interest because of the possible application to interplanetary dust particle (IDP) capture by spacecraft. We present a model for the phenomena occurring in such impacts into low-density organic polymer foams. Particles smaller than foam cells behave as if the foam is a series of solid slabs and are fragmented and, at higher velocities, thermally altered. Particles much larger than the foam cells behave as if the foam were a continuum, allowing the use of a continuum mechanics model to describe the effects of drag and ablation Fragmentation is expected to be a major process, especially for aggregates of small grains. Calculations based on these arguments accurately predict experimental data and, for hypothetical IDPs, indicate that recovery of organic materials will be low for encounter velocities greater than 5 km s-1. For an organic particle 100 μm in diameter, ~35% of the original mass would be collected in an impact at 5 km s-1, dropping to ~10% at 10 km s-1 and ~0% at 15 km s-1. For the same velocities the recovery ratios for troilite (FeS) are ~95%, 65%, and 50%, and for olivine (Mg2SiO4) they are ~98%, 80%, and 65%, demonstrating that inorganic materials are much more easily collected. The density of the collector material has only a second-order effect, changing the recovered mass by <10% of the original mass.