Ski resort problem

With the popularity of U-shaped snowboarding, there is an increasing demand for people to watch and appreciate the water products of the event, which requires athletes to make more and more difficult and graceful movements in the air, such as somersault, take-off with the front edge, grab the front board with the back hand, take-off with the back edge, grab the front board with the front hand and so on, and the completion of these movements depends on the height in the air. The shape of ski resort is the main factor affecting flying height. In order to solve the above problems, this paper takes the semi-tubular ski resort with semi-circular and power function curves as the research object. Taking the maximum vertical distance that a skater can reach as the goal, according to the principle of conservation of energy, the mathematical models of differential equations with partial semicircle and power function curves are established respectively: y = a×k, and then taking a figure skater as an example, their specific shapes are given under certain reasonable assumptions. Then, aiming at somersault in the air, an objective function is established to maximize the rotation angle while maintaining a certain height. By modifying the above surface, the height of the surface is appropriately reduced, and then a slightly downward slope is added to its upper edge. Through the establishment of the model, the correctness of the model is verified by the competition data of specific athletes. Finally, in order to make the model practical, the model is selected from four aspects: the U-shaped groove should have a certain inclination; Add a moderately wide plane to the bottom; Add a platform with appropriate width at the upper edge of the groove and a guardrail with appropriate height at the outer edge of the platform. The shortest length of U-shaped groove is given.