Our Task?

On October 10, 2023, we were assigned to find ways to improve athletic performance here at San Marin. We were given the option to choose our sports action and chose the most straightforward but most complicated part of baseball: hitting. Our goal was to help San Marin Mustangs become successful at the plate, using physics to explain every step thoroughly. We covered some significant physics concepts, including acceleration, velocity, vertical velocity, horizontal velocity, vertical distance, momentum, momentum transfer, elasticity, and air resistance. Additionally, we explained the ideal launch angle of the ball as it is essential to a successful swing. 

We introduced ourselves to our new group and learned about everyone's strengths and weaknesses. We started brainstorming ideas for our storyboard, organizing and filtering possible ideas. Once we finalized our storyboard, we recorded our sports action by taking slow-motion and close-up shots. Moreover, we found the horizontal distance of our calculation shots by hitting the ball on the fifty-yard mark of a football field and then measuring how far the ball traveled by having a teammate stand and watch. After completing our shots, we began to work on our calculations by first calculating the weight of the person who hit the baseball, as mass was a critical component when calculating concepts such as force and momentum. We were required to calculate the velocity before contact, the angle, horizontal, vertical, and total speed. Moreover, we were required to calculate the force of impact and the transfer of momentum in our motion. 

After completing every other aspect of the project, we transitioned to editing using the platform CapCut. We took all of our voiceovers and calculations, as well as our action shots and clips, and created a seamless video using the editing software. Additionally, we implemented various diagrams to show our understanding of the assignment and the material. The charts and calculations showed the audience proof that our advice was reliable and gave them the best advice to be successful at the plate. The result was a video that hopefully gave San Marin Mustangs the guidance they need to be successful at offense in baseball.

Evidence of Work

Content

REQUIRED:

1. Velocity Before Contact

2. Angle

3. horizontal velocity of _(ball, person, etc)____ =

4. vertical velocity of _______ =

5. total velocity (use Pythagorean theorem a^2 + b^2 = c^2) =

6. Force of impact (mv = Ft where t is the time of contact/push) =

7. Transfer of momentum

8. OTHER/OPTIONAL:

9. Spin/rotation

10. air resistance

11. elasticity

Velocity Before Contact

The ball's velocity before contact was seven meters per second or fifteen point seven miles per hour. We tossed the ball underhand from an angle, which resulted in a relatively slow entry velocity. The slow entry velocity resulted in variations in calculations as it rooted the foundation for other physics concepts included in the project. We calculated the entry velocity of the ball by dividing the distance it traveled, five meters, by the time it took to reach the batter.

Angle of Ball

The angle of the ball after impact was sixty-three point four degrees from the horizontal. Because the ball was launched at an angle from the horizontal, the initial velocity was affected because the ball now had a horizontal and vertical component, which included the force of gravity, nine point eight meters per second squared. We calculated the ball's launch angle using velocity vectors and the cosine function to get the final answer. The bat angle is an essential component of the swing, resulting in a farther hit, which could result in a home run.

Horizontal Velocity

Horizontal velocity is the speed of an object moving horizontally from side to side. In our project, the ball's horizontal velocity was fifteen meters per second or thirty-three point six miles per hour. We calculated the horizontal velocity by dividing the horizontal distance by the time the ball took to hit the ground. We incorporated the ball's horizontal velocity to create a vector diagram, which was very helpful when calculating the total velocity and the ball angle after impact. The greater the velocity, the farther the ball will go. The horizontal velocity is like any velocity, a vector quantity calculated by dividing the displacement, distance covered, by the time. However, we calculate it by dividing the distance by the time it takes to hit the ground. Vertical velocity is the vertical component of a velocity vector.

Vertical Velocity

Vertical velocity is an object's speed as it falls or goes up. The ball's vertical velocity was thirty meters per second or sixty-seven point ten miles per hour. We calculated the vertical velocity by multiplying the acceleration due to gravity by the time the baseball hit the ground. The vertical velocity is affected by gravity and air resistance, leading to a sooner drop-off in the motion. We incorporated the ball's vertical velocity into a vector diagram, which we used to calculate the total velocity of the baseball. The vertical velocity is similar to the horizontal velocity, the vertical component of a velocity vector diagram.

Total Velocity

Total velocity is the combination of the horizontal and vertical velocities or components. The total velocity of the ball was thirty-three point-five meters per second or seventy-four point-nine miles per hour. The total velocity is the hypotenuse, the longest side of a right triangle, of a velocity vector diagram. It is the combined velocities of both the vertical and horizontal components. We used the Pythagorean Theorem: a squared plus b squared equals c squared to calculate the total velocity. Leg a is the horizontal velocity, and leg b is the vertical velocity. The total velocity of the ball was realistic because the ball came in with a slow velocity.

Force of Impact

The force of impact is the force generated when two objects collide. The equation for calculating the force of impact is mv = Ft, where t is the time of contact or the push. In our project, we incorporated the force of impact between the bat and ball, which was 2220 newtons. As discussed earlier, the ball came in with a relatively slow velocity, resulting in a lower impact force. The ball generated little force because of the slow velocity. Regardless of the slow ball velocity, the bat still managed to achieve a large force and acceleration, making the time of impact zero point zero one second. To find the change in velocity, we subtracted the velocity before contact from the total velocity to bet us a velocity of thirty-seven meters per second. We then incorporated this information into our equation to calculate the force of impact.

Transfer of Momentum

The conservation of momentum states that the momentum put in before the collision equals the momentum after the collision. We used the equation MV+MV=MV+MV to calculate the velocity of the batter, which was moving at negative zero point zero five meters per second. The batter's velocity was negative because he was going against the ball in the opposite direction. Because momentum is conserved, the higher rate before contact with the ball will result in more momentum after the hit, causing the ball to go farther with incredible speed and acceleration.

Elasticity

Because momentum is conserved, we can assume that the bat transferred one hundred percent of its total energy to the ball. However, because there was an outside force working on the ball, the hitter, the motion cannot be one hundred percent elastic. Additionally, the activity can not be one hundred percent elastic because some kinetic energy is lost to heat and friction. Moreover, the ball might lose energy to air resistance. In this instance, the collision between the bat and the ball was twenty-four percent elastic, meaning the bat only exerted twenty-four percent of its total kinetic energy on the ball. The other seventy-six percent of the energy came from the hitter, portraying the importance of having good swinging form in baseball.

Air resistance

Additionally, a lot of energy could be lost to air resistance. Air resistance refers to the forces working against a projectile as it launches through the air. Air resistance affects the horizontal velocity component, causing a greater parabolic shape in the overall motion, negatively impacting the ball's distance. Additionally, the height of the ball might be negatively affected, depending on the severity of the drag.

Calculations

Analysis

The project went well as I developed strategies for working with my teammates. For instance, I learned to cope with failures within the group when one messed up the calculations or script, which delayed our project. I learned to be more sympathetic and empathetic throughout the project. This issue was something that I struggled with constantly throughout the Rube Goldberg Machine, and I am proud to say that it has improved. I began to show my teammates how to do the steps and calculations instead of taking over the whole operation and leaving them struggling in their academic journey. I also learned to divide the work more evenly throughout the project based on each teammate's strengths and weaknesses. I was very successful in my communication as everyone knew what they should do outside of school, portraying growth in my communication skills. I stayed in touch with each of my teammates and messaged them if I had a question or wanted them to work on something.

With that said, there are many aspects of the project that I could have improved upon, including my conscientious learner skills. Although I completed all of my portions of the project, I vastly underestimated the time it would take to edit the video, as I thought it would be the easiest part. I spent over sixteen hours editing the footage, making smooth transitions, and doing the voiceovers, including the clips and diagrams. I also had to watch many tutorials to learn to work with the editing software, which took up much class time. I later realized the editing software was easy to use with some practice. Moreover, I could have built a stronger relationship with my teammates as we sort of only talked about the assignment and the task at hand and spent little to no time trying to get to know each other. For these reasons, I could have improved my community builder and conscientious learner skills as they caused minor setbacks throughout our physics of sports project and video.  

Overall, the physics of sports project was immensely successful as it taught me to accept group failures and minor setbacks that delayed our project closer to the deadline. I am thankful that all my teammates were hard workers and understood the importance of a strong work ethic, significantly contributing to the project's success. Reflecting on our final product, it is safe to say that our project was a significant success as it taught us to accept and reflect on failures, making us better individuals along the way.