We study the stopping force felt by an intruder impacting onto a granular medium. Variations in the shape of the intruder can influence the penetration depth by changing the inertial drag. We find this observed correlation can be explained by associating the velocity-dependent inertial drag to the energy dissipation that occurs through intermittent collisions of force-chain-like clusters, the mean behavior of which can be statistically described. In consequence, the stopping force can be captured through a proposed collisional model with good accuracy, and the observed impact dynamics data can be reproduced quantitatively.