  In this analysis, we consider the effects of non-quiescent initial conditions
driven by pre-impact air-water interactions on the classical Wagner model of
impact theory. We consider the problem of a rigid, solid impactor moving
vertically towards a liquid pool. Prior to impact, viscous forces in the air
act to deform the liquid free surface, inducing a flow in the pool. These
interactions are then incorporated as initial conditions in the post-impact
analysis. We derive expressions for the size of the effective contact set, the
leading-order pressure and force on the impactor, and the speed and thickness
of the jet at its base. In all cases, we show that the effect of the pre-impact
behaviour is to cushion the impactor, reducing the size of the effective
contact set and, hence, the force on the impactor. Small- and large-time
asymptotic solutions are derived for general power-law impactors, and we show
that the effects of the air die away as the impact progresses, so that we
approach the classical Wagner solution.
