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本文从一道抛体的极值问题入手,对物理极值的数学应用做一点有益的总结,例题如下:如图1所示,从A点以某一初速度抛出一个小球,在离A点水平距离为s处有一堵高度为h的墙BC,不考虑空气阻力,问小球至少以多大的速度才能使小球恰好越过墙壁.三角函数类型解一当小球到达B点时,其位移矢量与水平面夹角为a且.如图2所示,将抛体运动视为沿初速度方向的斜向上的匀速直线运动和自由落体运动的叠加,由正弦定理得
This article starts from the extreme value of a projectile and summarizes the mathematical applications of the physical extremes. The following is an example: As shown in Figure 1, a small ball is thrown at an initial velocity from point A, Point at a horizontal distance of s has a height of h wall BC, regardless of air resistance, and asked the ball at least how much speed to make the ball just across the wall. Trigonometric function type solution When the ball reaches B, its As shown in Fig. 2, the projectile motion is regarded as the superposition of the uniform linear motion and the free-fall motion in the diagonal direction along the initial velocity direction, which is determined by the sine theorem