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1985年苏联举行的第十九届全苏中学生物理奥林匹克竞赛中有这样一道试题:足球运动员在11米远处的罚球点准确地从球门横梁下边沿踢进一球。横粱下边沿离地高度为 h=2.5米,足球质量为 m=0.5千克,空气阻力不计,必须传递给这个足球的最小能量 E_(min)是多少?原题及解答参见《物理教学》1987年第3期26页,参考解答是用导数求的。《物理教学》1988年第3期上所载《二次方程的判别式在求物理极值中的作用》一文中的例题1,作者选用了该题,是用判别式解的。本文笔者介绍一种简捷的巧妙的处理方法,借助于“两个实数之差的平方不小于零”的数学原理,可使解题过程大为简化。
In the 19th All-Soviet Junior Physics Olympiad held in the Soviet Union in 1985, there was a question: a football player accurately scored a goal from the lower edge of the goal crossbar at a penalty point 11 meters away. The height of the lower edge of the sky is h=2.5 meters, and the mass of the football is m=0.5 kg. Air resistance is not considered. What is the minimum energy E_(min) that must be passed to this football? For the original question and answer, see Physics Teaching 1987 Year 3, No. 26, reference answers are sought using derivatives. In “Physics Education”, Issue 3, 1988, the example 1 in the article “The role of the discriminant of quadratic equations in the search for physical extremum”, the author chose this question and used the discriminant solution. In this paper, the author introduces a simple and clever way of handling. With the help of the mathematical principle that the square of the difference between two real numbers is not less than zero, the problem-solving process can be greatly simplified.