\label{eqn:v_i}$$ and the angle of impact (measured from horizontal) is $$\theta_{impact}={\rm arctan}\left( \frac{\sqrt{v_{z,eject}^2 +  2 g dz}}{v_{x,eject}}\right). \label{eqn:theta_i}$$

The velocity and angle of impact along with classifications based on impact crater morphology were used to make Figure \[fig:ric\]. Figure \[fig:ric\] shows that crater morphology and impact behavior depends on both impact angle and velocity. At higher velocities and lower impact angles ricochets are more likely. Below a velocity of about 2 m/s grazing impacts had projectiles that rolled out of their crater rather than bounced off the sand. The dividing line between ricochet and roll-out and that between ricochet and stop was sometimes sensitive to vibrations and wobble in the apparatus. We noticed that the location of the ricochet/roll-out line shifted when we inserted shims into the pivot holder to keep it from vibrating during impact. With vibrations reduced, events were repeatable, with series of three or four trials at the same initial pendulum height and stop-bar position giving the same impact crater morphology and event classification. We tentatively assign a $\pm 5$ error to each point in Figure \[fig:ric\] that is due to variations in stiffness in the mechanical launch mechanism that we have tried to minimize. This value 