Study on the maximum value of flight distance based on the fractional differential equation for calculating the best path of shot put

From the perspective of physics, this article analyzes the various factors that affect the distance of shot put in the process of actual shot put. Based on the actual situation, it uses fractional calculus and physical formulas to calculate the shot throw distance and to conduct a comprehensive analysis. The experiment confirms that the three factors that affect the shot flying distance are the shot angle, shot speed, and shot height and analyzes the relationship between these three factors and the impact of each univariate on the shot flying distance. The analysis results show that among the three factors, the shot speed has the greatest impact on the flight distance, followed by the shot angle, and the shot height has the least effect; moreover, the optimal shot angle is not a specific value but a general range.