Using the gas drag by sublimating cometary surface ices for the acceleration of dust particles and deceleration by the gravity field of the nucleus combined with basic laws of mechanics, the sizes, velocities, and number densities of escaping particles are calculated and evaluated with respect to the hazard assessment of comet-spacecraft flybys and encounters. We find good agreement between our analytical method and the more elaborate and precise DSMC calculations, but, being simpler, our method can more easily be used to explore a wide range of cometary conditions and can be more easily scaled to specific comets with different nucleus sizes, masses, and gravity potentials and various gas and dust production rates. Our analytical method is applied to outbursts expanding into a cone of ~60°, where the gas density falls off with height from the surface rather than radial distance from the center of a uniformly outgassing nucleus. In this scenario, larger dust particles can be ejected and attain ballistic trajectories, go into orbit, or escape from the nucleus, thus being potentially more hazardous to a spacecraft. Sample calculations are carried out for potential dust outbursts for the highly active Centaur/Comet 29P/Schwassmann-Wachmann 1 for various assumed active areas and dust particle size distributions. Particle velocity ranges for ballistic trajectories, orbiting particles, and particles escaping into the coma are presented. These calculations are used to estimate the coma particle number densities during outbursts to get an assessment of the hazards and required mitigation for a flyby or orbiting space mission.