篮球罚球技术中“抛体运动方程”应用研究

Applied Research of the Projectile Motion Equation in Basketball Free Throw

通过体育学、运动力学等学科知识,从抛体运动方程出发,忽略空气阻力及其绕质心的转动的情况下,针对不同身高的篮球运球员给出一个合理的出手速度和角度范围。研究发现:1)在忽略空气阻力及其绕质心的转动的情况下,篮球在空中的运动可用其质心的运动来描述,即把篮球的运动视为为质点运动;2)在出手高度h一定的情况下,能投篮得分的出手速度v0和出手角度θ的区域Z,以及最小的出手速度v0min和最大出手角度θmax;3)罚球时以速度v0b、角度θb投出后,在投篮命中的前提下所允许的出手速度和角度的相对误差最大。

The study focuses on advising the basketball players on a reasonable release speed and angle range according to their heights at free throws. The suggestion is given by applying ＂the projectile motion equation＂, ignoring air resistance and its rotation about the mass center. The study finally concludes that： first, without consideration of the air resistance and its rotation about the mass center, the basketball movement in the air can be described by the movement of its mass center; second, with a definite release height h, a player scores only when the domains Z between the release speed v0 and the release angleθ; thrid, when a free throw is made at the speed vab and angle θh, on the premise that it scores, the relative error between the casting speed and the angle is to the maximum.