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在进行高中物理竖直上抛运动教学时,都会讲到下述例题: [例题]有一球从屋顶以14.7米/秒的速度竖直向上抛出,若屋高49米,试求此球落地所需的时间。本题通常都用二种方法求解:第一种方法是,把竖直上抛至落地过程分为上升和下落两个阶段而分别计算;第二种方法是直接利用位移方式,求解如下: [解]结合题意,选取座标如图1所示: 运用位移公式: h_1=v_0t+1/2 at~2 代入各量的值: -49=14.7t-1/2.9.8t~2 有 t_1=-2秒(舍去);t_2=5秒两种方法当然都得到该球从屋顶竖直抛出后5秒落地。在讲解过程中,尽管学生对于取坐标不会有太多的疑问,但对于计算中以“-49”代入位移公式左边,最后算得t=5秒,总感到仅是一种数学上的巧合,缺少物理概念,因而不够信服。
In the high school physical vertical throwing exercise teaching, will mention the following example: [example problem] there is a ball from the roof with a speed of 14.7 meters / second thrown vertically, if the house is 49 meters high, try to find the ball landing The time required. This problem is usually solved by two methods: The first method is to separate the vertical up and down process into two phases: rising and falling, and calculate separately; the second method is to directly use the displacement method and solve the problem as follows: ] Combining problem meanings, select the coordinates as shown in Figure 1: Using the displacement formula: h_1=v_0t+1/2 at~2 Substituting values for each quantity: -49=14.7t-1/2.9.8t~2 With t_1= - 2 seconds (throw away); t_2 = 5 seconds Both methods, of course, get the ball landed 5 seconds after it is thrown off the roof. In the course of explaining, although students do not have too many questions about taking coordinates, for the calculation, the substitution of “-49” into the left of the displacement formula, and finally calculated t=5 seconds, always feels only a kind of mathematics. Coincidence, lack of physical concepts, and therefore not convinced.