  When an intruder strikes a granular material from above, the grains exert a
stopping force which decelerates and stops the intruder. Many previous studies
have used a macroscopic force law, including a drag force which is quadratic in
velocity, to characterize the decelerating force on the intruder. However, the
microscopic origins of the force law terms are still a subject of debate. Here,
drawing from previous experiments with photoelastic particles, we present a
model which describes the velocity-squared force in terms of repeated
collisions with clusters of grains. From our high speed photoelastic data, we
infer that `clusters' correspond to segments of the strong force network that
are excited by the advancing intruder. The model predicts a scaling relation
for the velocity-squared drag force that accounts for the intruder shape.
Additionally, we show that the collisional model predicts an instability to
rotations, which depends on the intruder shape. To test this model, we perform
a comprehensive experimental study of the dynamics of two-dimensional granular
impacts on beds of photoelastic disks, with different profiles for the leading
edge of the intruder. We particularly focus on a simple and useful case for
testing shape effects by using triangular-nosed intruders. We show that the
collisional model effectively captures the dynamics of intruder deceleration
and rotation; i.e., these two dynamical effects can be described as two
different manifestations of the same grain-scale physical processes.
