考虑空气阻力的抛体最大射程和最佳抛射角研究

为了研究抛体在什么抛射角抛出时具有最大射程,利用拉格朗日乘子法,推导出存在空气阻力并且起点和终点不在同一高度时,在某一斜面上抛出的抛体的最大射程和最佳抛射角.通过计算机编程,以计算投掷手榴弹时的最大射程和最佳抛射角为例进行验证,并对物理教学中抛体运动的动力学过程进行了进一步的分析和讨论,有利于提高教学效果.

Study of Maximum Range and Optimum Projection Angle of Projectile With Air Resistance

In order to study the projectile can have the maximum range at what projection angle,the air resistance existed was deduced by using Lagrange multipliers,and the optimum projection angle and the maximum range of the projectile projecting out of some inclined plane were given.the maximum range and the best angle when the starting point and end point being not at the same height were deduced.By computer programming,it was verified by taking an example of calculating the maximum range and optimum projection angle while projecting grenades,by which the kinetics process of projectile motion in physics teaching was analyzed furthermore,helping improve the teaching effect.