  We compute the distribution of velocities of the particles ejected by the
impact of the projectile released from NASA Deep Impact spacecraft on the
nucleus of comet 9P/Tempel 1 on the successive 20 hours following the
collision. This is performed by the development and use of an ill-conditioned
inverse problem approach, whose main ingredients are a set of observations
taken by the Narrow Angle Camera (NAC) of OSIRIS onboard the Rosetta
spacecraft, and a set of simple models of the expansion of the dust ejecta
plume for different velocities. Terminal velocities are derived using a maximum
likelihood estimator.
  We compare our results with published estimates of the expansion velocity of
the dust cloud. Our approach and models reproduce well the velocity
distribution of the ejected particles. We consider these successful comparisons
of the velocities as an evidence for the appropriateness of the approach. This
analysis provides a more thorough understanding of the properties of the Deep
Impact dust cloud.
