  Experiments on the low-speed impact of solid objects into granular media have
been used both to mimic geophysical events and to probe the unusual nature of
the granular state of matter. Observations have been interpreted in terms of
conflicting stopping forces: product of powers of projectile depth and speed;
linear in speed; constant, proportional to the initial impact speed; and
proportional to depth. This is reminiscent of high-speed ballistics impact in
the 19th and 20th centuries, when a plethora of empirical rules were proposed.
To make progress, we developed a means to measure projectile dynamics with 100
nm and 20 us precision. For a 1-inch diameter steel sphere dropped from a wide
range of heights into non-cohesive glass beads, we reproduce prior observations
either as reasonable approximations or as limiting behaviours. Furthermore, we
demonstrate that the interaction between projectile and medium can be
decomposed into the sum of velocity-dependent inertial drag plus
depth-dependent friction. Thus we achieve a unified description of low-speed
impact phenomena and show that the complex response of granular materials to
impact, while fundamentally different from that of liquids and solids, can be
simply understood.
