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

Xiang Zhang

Xiang Zhang

Northwest University of Political Science and LawShaanxi, China
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Zhang, Xiang
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Dimah Alahmadi

Dimah Alahmadi

Department of Information Systems, Faculty of Computing and Information Technology, King Abdulaziz UniversityJeddah, Saudi Arabia
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Alahmadi, Dimah
  
30. Dez. 2021
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Online veröffentlicht: 30. Dez. 2021
Seitenbereich: 151 - 162
Eingereicht: 17. Juni 2021
Akzeptiert: 24. Sept. 2021
DOI: https://doi.org/10.2478/amns.2021.2.00136
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© 2021 Xiang Zhang et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Shot parameters (shot speed) and trajectory
Shot parameters (shot speed) and trajectory

Fig. 2

The coordinates of the shot put
The coordinates of the shot put

Fig. 3

The coordinates of the shot motion when considering air resistance
The coordinates of the shot motion when considering air resistance

Fig. 4

Schematic diagram of each speed vector
Schematic diagram of each speed vector

Judging extreme points

x (0, e) e (e, ∞)
F′(x) A positive number 0 Negative number
F(x) Increasing F(e)=22 F(e) = 2\sqrt 2 maximum Decrement

Shot put results and shot angles of world-class shot putters

Name Shot put results, m Shot angle, °
Li Meisu 20.3 38.69
20.95 37
21.76 35.13
Huang Zhihong 20.76 37.75
21.28 41.3
21.52 36.9
Slupianek 21.28 41.3
21.41 40
22.45 36
Sui Xinmei 21.66 39
Lisovskaya 20.86 42.6
Bayer 21.02 34.1
Gunther 22.23 35.5
Timmerman 21.35 35.8

Combination modes of shot flying distance, shot speed, shot angle, and shot height

Speed of shot, m/s Shot height, m Shot angle, °
36 37 38 39 40 41
11 2 14.044 14.102 14.192 14.181 14.2 14.207
2.05 14.094 14.15 14.237 14.226 14.245 14.25
12 2 16.33 16.409 16.54 16.521 16.554 16.571
2.05 16.382 16.459 16.586 16.569 16.6 16.616
13 2 18.802 18.904 19.08 19.054 19.102 19.131
2.05 18.855 18.956 19.129 19.103 19.15 19.177
14 2 21.461 21.589 21.781 21.781 21.845 21.887
2.05 21.516 21.642 21.831 21.831 21.894 21.935
15 2 24.308 24.464 24.747 24.703 24.785 4.841
2.05 24.364 24.519 24.797 24.754 24.835 24.89
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