Abstract: Based on the resistance model，this paper analyzes the classical penetration dynamics problem of an unpowered ball motion with initial velocity on a granular medium by introducing inertial resistance，viscous resistance and static resistance derived from Archimedes- modified law. A quantitative solution of the longest sliding distance of the pellet on the particle medium is obtained by means of the kinetic equation of the pellet motion. The particle density ρ_0，particle packing densityρs，particle radiusr，sphere radius R，sphere density ρb，Youngs modulus G of the particle medium are also investigated. And the influence of initial velocity v0 on the distance of small ball. It is found that the theory of resistance model is in good agreement with the experiment.

Key words: penetration dynamics, resistance model, kinetic analysis, maximum distance quantitative solution