Ballistics with Linear Drag and Inelastic Collision — Distance, Impact Speed, Energy Loss, Rise Height
A projectile moves horizontally with linear air drag causing an exponential speed decay. The travel distance to the target links launch speed damping time and flight duration. Impact speed at the target follows a simple relation between launch speed distance and damping time. A totally inelastic hit conserves linear momentum but reduces kinetic energy. The energy loss equals the reduced mass times the square of the impact speed up to a factor. After impact the joined masses rise and convert kinetic energy into gravitational potential. The peak height depends only on the post-impact speed and gravity
Angular momentum about the hinge just after impact equals lever arm times post-impact momentum with direction set by the right-hand rule. During the very short collision the external torque about the hinge is effectively zero. Once the system starts rising gravity provides a nonzero external torque and angular momentum changes.
