Mathematical and Physical Analysis of the Shooting Techniques of High-pole Throwing Hydrangea

: By using the methods of literature and mathematical analysis, the present representative technical theory of high-pole throwing Hydrangea is analyzed, this paper analyzed the technical movements of the high-pole throwing Hydrangea of technology, such as the angle, speed and height of release of the athletes, as well as the running track data of the parabolic arc top height, the range of passing circle and the place of falling of the high-pole throwing Hydrangea champion in the 12th Guangxi Student Games in 2019. The results show that: the range of the angle of release is 64 0 ≤ α ≤ 72 0 ; when the angle of release is 64 0 lower limit, the velocity of release is v 0 ≥ 13.04m/s lower limit, when the ball reaches the highest point, it passes through the lower edge of the circle. When the angle of release is 72 0 upper limit, the velocity of release is v 0 ≥ 13.17m/s , the top of the arc of the ball is 1.8m away from the top of the circle, and it passes through the lower edge of the circle when it falls; when the angle of release is 66 0 , the velocity of release is v 0 ≤ 13.70m/s upper limit and the ball passes through the upper edge of the circle when it rises to the highest point; under the three circumstances, the arc top of the ball does not exceed the circle, and the height from the ground does not exceed 10m. At the same time, it proves the scientificity and reliability of the projection technique of Hydrangea.

Among them, the most representative are:the best initial velocity V0 =16.3m/s, and the best passing point is the center of the passing circle. [4][5] [6] It was shown in figure 1. These theories have a very good technical and theoretical guidance for the ball to pass the circle smoothly, but the prediction of the highest point of the ball, the falling point of the ball and the next shooting situation is not enough, and the consideration is lack of coherence, so it is lack of guiding significance for highlevel games. According to the rules of performance evaluation, the winner is the one with more hits per unit time. According to the dominant factors of competitive ability, high-pole shot Hydrangea belongs to the accuracy item of skill and mental ability. According to the classification of action structure, it belongs to the fixed combination project of multiple action structure and has obvious periodic characteristics. Therefore, according to the rules of the game, we must complete more projection times in unit time and improve the hit rate in order to win the game, which is a test of athletes' psychology, skills and physical fitness.   This representative projection technique can solve several situations of hand projection range and crossing circle, but the height of projection, landing time and horizontal displacement increase, and the whole projection period is prolonged.

The contradiction between competition rules and existing theories
Players can score points by throwing the Hydrangea over the pitching circle within the specified time. After each throw, they should run to the opposite pitching area to pick up their own ball and continue to throw the circle. The middle circle will get 1 point at a time. In this way, the players can repeatedly throw the ball in the two bowling areas. In the specified time, the number of shots in the middle circle will determine the merits and demerits. [5] As shown in Figure 1  /t=16/ 16/g In the same way：v1sinα 1/v1cos α 1=tan α 1=16/7，the result is α 1≈66 0 ，v1≈13.70m/s

When the ball passes through point A 10m from the horizontal and passes through point C at the inner lower edge of the circle
h=7m，t2=(t+t3)The sum of the ascent of 8m to A and the fall of 1m to C is equal to，then t2= ( 16/g + 2/g ) Horizontal displacement： 7=v2cosα 2t2， then v2cosα 2= 7/ ( 16/g + 2/g ) The vertical displacement to A：8=v2sinα 2t-1/2gt 2 ，then v2sinα 2=8+1/2gt 2 , Substitute t= 16/g ，the result is ：v2sinα 2=16/ 16/g (5) simultaneous (4)  3.2 When the arc top of the ball is 10 m and falls through the inner and lower edge of the circle, the distance from the top of the arc to the top of the circle is 1.80 m, and the angle of release is the largest, α ≈72 0 . The speed of release is 13.17m/s, less than this speed, the ball can not pass through the circle, and higher than this speed, the ball will fall through the arc top E. Therefore, in the maximum angle of release, the speed should be large rather than small. Although the increase of height will prolong the time of falling, it is conducive to running and catching the ball calmly.
3.3 When the top of the ball passes through the upper edge of the circle, the angle of release is α 1≈66 0 , and the velocity reaches the maximum value, V ≈ 13.70m/s. This is the combination of angle and speed, which is the farthest and takes the longest time among the three shooting methods. The distance between the landing point D and the projection point O is 14m, which is the same as the first case in 3.1 above, but the time is longer, which is the time consuming for 8m high falling.

4.2
The angle of the shot is better high than low, because you can't score a goal below 64 0 , and the high angle can go into a circle in the falling process. When the release angle is 66 0 , the maximum value of V ≈ 13.70m/s is taken as the boundary, and the projection speed V gradually decreases to 13.04m/s when it goes down to 64 0 and to 13.17m/s when it reaches 72 0 .