Cases that are reliably witnessed or captured on film or documented with a suicide note can generally be handled by the police and the coroner orthe courts, without the assistance of expert advice. In other cases, the question that needs to be answered is whether the fall was the result of an accident, suicide, or homicide. Did the victim accidently slip, trip, or overbalance, or deliberately jump or dive, or was the victim pushed or thrown? In some cases the police want to know whether a witness or a suspect has given a plausible version ofthe event. The trajectory of a fall is important, but there are other aspects of a fall, such as the launch and landing phases of the fall, which can also be investigated using physical measurements and calculations. These include measurements of the speeds at which a person can run, jump, dive, be pushed or thrown, an estimate of the rotational speed associated with each launch method,measurements or estimates of runup and takeoff distances, calculations of possible trajectories based on different launch angles and wind speeds, location of the center of mass of a person on video data, and an analysis of possible bounce and impact events. When all the data are combined with other evidence obtained by the police and medical specialists, the circumstances surrounding a fall can sometimesbe determined accurately. Often, there is insufficient evidence to arrive at a definite conclusion.

TRAJECTORY CALCULATIONS Suppose that a person lands at a horizontal distance d=9 m from a building after falling from a height h=30 m. The fall time is = 2ℎ/ = 2.7 s and the horizontal launch speed is vx=dt=3.64 ms. If the only possible launch point was a narrow ledge below an open window,could a person jump at 3.64 ms from a standing start, dive, or be pushed or thrown through the window at that speed? To answer this question we would first need to improve on the estimate provided by the simple physics calculation. We would then need to take measurements of typical jump, dive, and throw speeds, appropriate for the estimated athletic ability of the deceased and any known suspects.The horizontal distance traveled by a person from a given launch point to the first point of impact has three components consisting of the takeoff, flight, and landing distances. The flight distance is the horizontal distance traveled by the center of mass of the person through the air. The takeoff distance, dT, is the horizontal distance from the center of mass to the foot on the ground at theinstant that the person becomes airborne. The center of mass could be 0.5 m beyond the edge of a cliff or building when the person first becomes airborne. The landing distance, dL, is the horizontal distance from the center of mass to the first point of impact, and may also be around 0.5 m. The horizontal launch speed required to jump a horizontal distance of 1 m is therefore zero because a person cansimply step that distance at essentially zero speed. Suppose that the center of mass of a person falls through a vertical height H and travels a horizontal distance D through the air, as shown in Fig. 1. If we ignore the effects of air resistance or wind, then H and D are related to the launch speed v0 and the launch angle θ0 by

which reduces to the well known result D=v0 2 sin_2_0_ g when...