Abstract
In long jump, it is possible to estimate a distance between takeoff and landing by assuming that the center of mass of a long jumper in aerial phase moves along a trajectory of projectile. Based on the assumption, we obtain an approximate trajectory of the jumper as a perturbed solution of flat aerial path, in which the effect of air drag is included as the linear form. Also, a maximization problem is formulated from the trajectory and the optimum angle of takeoff is theoretically derived. Then, we introduce two parameters, the horizontal velocity of the center of mass and the takeoff velocity into the present model of takeoff. In particular, the solution of the optimum angle includes the effect of vertical displacement at landing which affects significantly a distance of the aerial phase. The distance of the aerial phase and the takeoff angle are estimated in several cases of measured data. The results of the estimation show the effectiveness of the present solutions.
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