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This paper presents a unique derivation of airborne trajectory analysis equations from the classical physics equations of uniformly accelerated motion. These trajectory analysis equations are applied to an example problem with realistic real world values. A current widely utilized equation of human trajectory analysis ignores an important cosine function in the calculation of horizontal launch velocity. It is shown that ignoring this cosine function can yield significant error in calculations. A graph is derived from published data on freefall sky diving. This graph can be referenced to adjust calculated velocities for the effects of air drag. It is shown that prior published data which has been widely utilized within the accident reconstruction profession, is inaccurate. A simple method for the application of the derived equation and data to real world problems is outlined.

The Combined Airborne Tumbling Analysis Procedure Using Laws of motion to determine Throw speed (CATAPULT) for a pedestrian is compared to the published results of vehicle/pedestrian impact testing. Testing by the authors demonstrating the mechanics and dynamics of an object tumbling to rest following a known trajectory is presented. It is shown, that although during ground tumbling individual impulses of a pedestrian with the ground are what slow the pedestrian, with restitution occurring between these impulses, the use of an average drag factor of 0.5 over the total distance tumbled produces accurate results for initial speed.