Projectile Motion of Golf Trajectory

Projectile Motion of Golf Trajectory

By Zhanbo Chen, Stefan Deditoiu, Gonzalo Gil-Ortega, Alban Olivas, and Volodymir Voropai.

What is Projectile Motion?

• When an object is propelled into the air, its motion is referred to as projectile motion.
• It is solely affected by gravity and, if any, air resistance.
• The motion is two-dimensional, and its trajectory's vertical and horizontal components can be used to characterize it.
• A projectile trajectory is the curving route that an object takes when it is propelled at an angle to the horizontal.

What is Projectile Motion?

• When an object is propelled into the air, its motion is referred to as projectile motion.
• It is solely affected by gravity and, if any, air resistance.
• The motion is two-dimensional, and its trajectory's vertical and horizontal components can be used to characterize it.
• A projectile trajectory is the curving route that an object takes when it is propelled at an angle to the horizontal.

Why Projectile Motion?

We chose to create an experiment about projectile motion because this topic is in charge of explaining many aspects of the universe, ranging from jumping to falling. When we were sure that we wanted to study projectile motion, we then needed to decide which specific part of it we wanted to explore. Since golf balls are visible and produce a regular motion, they were the best option for us.

To inform ourselves and be able to carry out our experiment successfully, we first researched for information online.We also researched about how to use "Tracker", an app that lets us process the ball's video into a table and a graph of its motion.

Method and Materials

Materials

Method

• 1 Standard Golf Ball • 1 Standard Golf Bat • 1 Mobile Phone with Camera • 1 Computer

1. Launch the golf ball into the air using a golf bat.
2. Install the 'Tracker' app for video analysis.
3. To process the video, mark the ball's position in each frame, establish a reference distance, and select the coordinate axis to define position 0 and determine the values of X and Y.
4. Verify the accuracy of frame marking by examining the parabolic shape of the graph generated by the app.
5. Export the X and Y values, as well as velocities and accelerations, per frame for further analysis.

Data Processing

Based on the values "Tracker" gave us of the golf ball's movement, we calculated the theoretical approach:For the expected X distances, we used a ULM formula: x = xo + v.t. For Y values, we used a UALM formula: y = Yo + Vo.t + 1/2 A.T^2. With all this data, we made a graph in Excel comparing the practical approach to the theoretical approach.

Data Analysis

When the data was processed into graphs and tables, we then analyzed the results and made the following conclusions:

Additionally, the golf ball exhibited a lower trajectory in practical measurements, likely due to air resistance impacting both horizontal and vertical velocities.

The calculated X-axis movement fell short of its actual distance, attributed to the oversight of not accounting for air resistance in our calculations.

Unconsidered factors such as aerodynamic properties, wind conditions, spin rate, and environmental factors potentially influenced the ball's movement in an unpredictable manner.

Applications

Analysing projectile motion and being able to predict it has many applications in diverse fields. In sports, such as soccer and basketball, players utilize the principles to enhance accuracy during free kicks and shots. Military and defense sectors use this knowledge for artillery targeting and missile systems design. Aerospace engineers apply projectile motion calculations for planning rocket launches and landing, ensuring accurate trajectories and orbital paths. In the entertainment industry, video game developers and filmmakers use the principles to create realistic simulations of object movement. Search and rescue operations benefit from projectile motion analysis when dropping supplies accurately in remote areas. The diverse applications of projectile motion analysis highlight its relevance in many aspects.

Projectile Motion in Celestial Bodies

In 1971, NASA astronaut Alan Shepard, Apollo 14 commander, played golf on the Moon. As a result of the Moon's low gravity and very disperse atmosphere, the balls traveled tens of meters. This was in spite of Shepard's lacking mobility due to his spacial suit, and of the fact that he hit the balls with an excavation tool. His idea invites us to explore how projectile motion would vary in different planets with their respective gravities and air resistances.

Improvements

Our experiment and its method was not perfect, so it has some possible improvements.

Extend the theoretical approach to cover hypothetical situations with different gravities, air resistances, etc.

Take into account the aspects we omitted in our calculations, like the ball's aerodynamics, spin, and the air resistance.

Make sure the video is always focused and of high frame/pixel quality

Make sure that the video is completely horizontal and evenly panned.

Conclusion

Overall, projectile motion has several applications in real life; however, in order to effectively apply it, a certain degree of trial-and-error must take place. Fortunately, a guideline to making effective projectile motion exists in the form of theoretical knowledge. Thus, by analyzing and comparing theory with experiments, one can identify inaccuracies and solve them to create a more effective solution.

Let's play a Kahoot!

https://create.kahoot.it/share/projectile-motion/1862c461-42aa-4c0e-a2bd-67bd45e338d1