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Discus Throw is a track and field event and competitors played solo in the competition. The performance of the player depends on the physical strength of the competitors. This game requires high coordination and precision of the athletes. A discus of weight 1 to 2 kg is thrown by the athletes into the air as beyond as he or she can within a remarked zone. The athletes throw the discus within a circular area of a 5-meter radius. The throw can be counted invalid if the discus lands far from the zoned boundary. The throwing demands high body balance, the grip of the discus, and a precise circular movement. The game is based on projectile motion. Two-dimensional kinematics of projectile motion represents the path of the discus after the throw. The two-dimensional kinematics of the discus throw is discussed in this report. How the performances of the athletes can be improved by the proper knowledge of kinematics are also analyzed here.

The above figure represents the trajectory of motion after the throw by going an initial push and being left alone to fall through gravity. After the throw, the discus is projectile motion in which the trajectory path of the object is parabolic (Wang *et al. * 2018). In the discus throw the initial velocity, initial angle, and the initial throw height plays an important role in the performance of the athletes.

Here is the height of the athlete, is the initial velocity of the discus, ? is the initial angle of launch at which the discus thrown, is the final velocity of the discus reaching at the target distance, h is the maximum height that the discus can achieve, and R is the range of the flight of the discus.

The horizontal distance =

And the vertical distance =

The equation of motion of the projectile is

y = - ½ g + * t + … (i)

The position of the discus after 0.75 seconds will be from equation (i)

= + * 0.75 – ½ g * (0.75)^2

Or, = + 0.75 - 0.28g

The velocity of the discus is

v = - g*t … (ii)

The velocity of the discus after 0.75 second will be from equation (ii)

v = – g * 0.75

Or, v = – 0.75g

When the discus reaches the maximum height from the ground, it stop moving upwards and starts falling, i.e. it velocity become zero at the maximum height (Xu *et al. * 2018). Let at the time the discus reaches maximum height.

Therefore, – g * = 0

Or, = /g

The vertical distance of the discus at that time is

h = * – ½ g *

Or, h = ½ g

Or, h = /2g

As the discus is thrown from initial height then, the maximum height that the discus can reaches,

h = + /2g

The time taken to reach the maximum height

= /g

Or, = /g

At the maximum height the velocity of the discus is zero as it stops moving upwards and starts falling (Yuliati and Mufti, 2020).

The equation of motion of the projectile at the initial point is

- = - ½ g + * t

Or, ½ g - * t - = 0

Or, ½ g - * t - = 0

Or, t = []/g

The range of flight is the horizontal distance covered by the discus during the flight.

Therefore, R = * t

Or, R = * t

Or, R = () * []/g

Or, R = () []

The time taken by the discus after the throwing and before it reaches to a horizontal plane is the total time of flight of the discus (Mungan, 2018). In this time the flights of the discus is ended which means the vertical distance of the discus from the ground is zero.

Therefore, - ½ g + * t + = 0

Or, ½ g = * t +

Or, ½ g – ( * t + = 0

Or, t = []/g

The velocity of the discus at any point of its projection is

v =

Where = and = - gt

Therefore, v =

The time when discus reaches the target is t = []/g

Therefore, the velocity =

Or, =

From the above calculation, it is seen that the range of flight of the discus from the through to the target distance is directed proportional to the initial velocity, throw height, and the throw angle. So, every value contributes to the flight range of the discus throw (Chen *et al. * 2021). The main aim of the discus throw is to increase the range of flight. The adjustment of every above-mentioned value can increase the range of flight.

- Among all of them, the initial velocity of the discus plays a greater role in the range of flight. The initial velocity of the discus throw further depends on the two factors such as the center of mass of the body of athletes’ velocity of the wrist of the athletes relative to the other parts of the body.
- From figure 2, it is seen that hope of the range of flight depends on the initial throwing angle. The value of the initial throwing angle around 45 degrees generates the maximum range of flight (Genço?lu and Gümü?, 2020). The value of the throwing angle greatly differs from 45 degrees than the range of flight decreases.
- For a given size and weight of the discus, the maximum initial velocity and the angle of the initial throw around 45 degrees can give the maximum value of the range of flight. The maximum height of flight cannot give the maximum range of flight.
- This game greatly depends on the physical fitness and physical strengths of the athletes, this helps to increase the initial velocity of the throw (Noh
*et al.*2019). The angle of throw also depends on how the athlete balances himself at the time of throwing. By maintaining all the above factors athletes can throw the maximum distance of their capability.

In the discus throw, two forces can alter the value of the discus flight; these are the force due to the speed of the wind and the force of gravity. The above calculations are done by considering the force of gravity. The force of the wind can be separated into specific directional forces. The aerodynamic forces act against the throw of the discus in the direction against the oncoming force (Dastgir, 2021). The force perpendicular to the direction of the oncoming force is called the aerodynamic lift. When the oncoming air is separated into two regions the lift is created and this created separate regions above and below the discus. In this situation, the air around the discus is flowing at different speeds and the discus starts to act as an airfoil. The pressure around the discus becomes different and the low pressure around the discus pushed upward direction and the range of flight decreases as a result.

The velocity of the wind may differ in the range of the flight. It is finding that athletes can achieve longer throwing against b wind than with no wind or the wind. The range of throws increases due to the larger lift and due to the drag the value decreases (Landell-Mills, 2019). But when the velocity of the wind is high, then the discus will not fly forward, it will stop or fly back. In a slight headwind, a longer range can be achieved than in the tail wind. With the tailwind maximum range can be achieved by increasing the initial throw angle.

The discus throw is a solo game based on the track and field event. Apart from the higher physical fitness, physical strength, and a great balance of the body the two-dimensional kinematics of physics plays a great role in the performance of the athlete. The game is about to increase the range of flight i.e. the horizontal distance of the target from the position of the throw. The range of flight directly depends on the initial velocity of the discus, the initial angle of throw, and the initial vertical height i.e. the height from which it throws. Among all of them, the initial velocity is an important factor because it is related to the center of mass of the body of the athlete and the velocity of the wrist relative to other parts of the body. The initial angle of throw around 45 degrees can give maximum range with the ideal condition. Aerodynamic drag and velocity of the wind can affect the range of flight. It is shown that with a slight headwind a larger range can be achieved.

**Journals**

Chen, C.F., Wu, H.J., Yang, Z.S., Chen, H. and Peng, H.T., 2021. Motion Analysis for Jumping Discus Throwing Correction. *International journal of environmental research and public health*, *18*(24), p.13414.

Dastgir, G., 2021. *Computational fluid dynamics simulation of flying discs* (Master's thesis, uis).

Genço?lu, C. and Gümü?, H., 2020. Standing handball throwing velocity estimation with a single wrist-mounted inertial sensor. *Annals of Applied Sport Science*, *8*.

Landell-Mills, N., 2019. How frisbees fly according to Newtonian physics. *Pre-Print DOI*, *10*.

Mungan, C.E., 2018. Solving a projectile motion problem by thinking like a physicist. *Physics Education*, *53*(6), p.063003.

Noh, S.A., Baharudin, M.E., Nor, A.M., Saad, M.S. and Zakaria, M.Z., 2019, November. A review of motion capture systems for upper limb motion in throwing events: Inertial measurement unit. In *IOP Conference Series: Materials Science and Engineering* (Vol. 670, No. 1, p. 012051). IOP Publishing.

Wang, Y., Zhou, J.H., Deng, X.X. and Zhong, S., 2018. Kinematic Analysis on the Final Exertion Motion of Elite Chinese Female Discus Throw Athletes. *DEStech Transactions on Social Science, Education and Human Science*, (emss).

Xu, J. and Zhang, W., 2018, August. Comparative Analysis of Kinematics of the Last Exertion Technique of Chinese Elite Female Discus Throwers. In *2018 2nd International Conference on Education Science and Economic Management (ICESEM 2018)* (pp. 688-691). Atlantis Press.

Yuliati, L. and Mufti, N., 2020. Acquisition of projectile motion concepts on phenomenon based physics’ experiential learning. In *Journal of Physics: Conference Series* (Vol. 1422, No. 1, p. 012007). IOP Publishing.

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