abstract: The research aims to build a mathematical model to conduct a static and dynamic force analysis of the starting position in a 50-meter freestyle for [4] swimmers .In order to unveil the truth of what the lines of reaction force foot do during the support and impulse phases, and then calculate the resultant of that force to rule the extent of the player's ability to employ an action line, of the resultant of the force of the foot towards the center of gravity, and at the same time the researcher tries to calculate the optimum take-off angle in theoretically by drawing a mathematical relationship between the take-off angle and the maximum horizontal distance while verifying the validity of the mathematical model, through the practical application of the model and a comparison between the results of the traditional take-off angle and the optimum take-off angle.
Keywords: static and dynamic force ; lines of reaction force ; optimum angle take-off