Using the discrete element method, we study the splash processes induced by the impact of a grain on a randomly packed bed. Good correspondence is obtained between our numerical results and the findings of previous experiments for the movement of ejected grains. Furthermore, the distributions of the ejection angle and ejection speed for individual grains vary depending on the relative timing at which the grains are ejected after the initial impact. Obvious differences are observed between the distributions of grains ejected during the earlier and later splash periods: the form of the vertical ejection-speed distribution varies from a power-law form to a lognormal form with time; this difference may determine grain trajectory after ejection.