CALCULATION AND VISUALIZATION OF A MAN PARACHUTING DOWNWARD

Abstract

The article suggests the calculation and visualization of motion of the man by opened and closed parachutes. It contains the formulation of the problem, the physical analog and mathematical model of the motion by closed and opened parachutes, the study of the kinematics and dynamics of the motion, the conditions for safe landing. There are graphs of the height versus time of motion and velocity versus height. The graphs show that the man falls down without parachute he reaches the Earth surface with the speed more than 30 m/s or 100 km/h. This is a dangerous descending. Landing is safe when the landing speed is of about u » 5 m/s. Duration of the landing time by the opened parachute is 34 min, and by the closed parachute the landing time is 3 min. The article also presents the calculation and visualization of the parachutist’s motion during free-fall drop when parachute opens in 20 seconds after the free fall start and the graphs of the height versus time and velocity versus height. It is seen from the graphs that at first the parachutist falls down with increasing speed reaching its upper value of about 40 m/s with which he proceeds his falling down within certain duration of time and at the height of 5400 m where the parachute opens the speed of the parachute sharply decreases and then gradually and monotonically reaches its value that enables a safe landing of the parachutist. Results of this study are used in classes on “Theoretical mechanics” and “Simulation of physical processes”.