The recent discovery of an enriched metallicity for the Smith high-velocity H I Cloud (SC) lends support to a Galactic origin for this system. We use a dynamical model of the galactic fountain to reproduce the observed properties of the SC. In our model, fountain clouds are ejected from the region of the disc spiral arms and move through the halo interacting with a pre-existing hot corona. We find that a simple model where cold gas outflows vertically from the Perseus spiral arm reproduces the kinematics and the distance of the SC, but is in disagreement with the cloud's cometary morphology, if this is produced by ram-pressure stripping by the ambient gas. To explain the cloud morphology, we explore two scenarios: (I) the outflow is incline...