Math Project Essay

The Best Drive Agnes Kwon, Jennifer Hwang

A. Overview
Our project focused on discovering the best angle a field hockey stick should be, relative to the ground, in order to achieve the best distance on a controlled drive. In order to test our experiments, we built a contraption to model a field hockey player’s swing. Our controlled variables included a 35” field hockey stick, a constant height for the back swing, and obviously, the structure of the contraption itself.

B. Methodology
In order to figure out how to answer our question, we went back to the fall season and thought about how we would regularly drive a ball in field hockey. We both had the common problem that our drives weren’t that consistent, so we realized that what probably changed was the position of our stick. Now that we recognized the problem, we thought about the math. If the player was standing straight, which ideally she should be, and the stick was touching the ground a certain length in front of her, it would simply form a right triangle. We thought back to Geometry and the SOH-CAH-TOA equations, the Law of Cosines, and all the rules we learned about angles in a triangle. As for the “side” lengths for the triangle, we decided to keep one of them, the stick length, constant and then change the distance from the player’s feet to where the stick touches the ground which would ultimately change the angle. Realizing that the calculations involved for our experiment weren’t too difficult, we thought about HOW we were going to experiment and get those numbers we needed to calculate the angle at the very end. At the first check-up with Mr. Jain, he suggested that we talk to Mr. Pinta, who could help us build some sort of 3D model to represent a field hockey player, so that we could eliminate a lot of the human variables that would change such as power, stance, feet movement, etc. Mr. Pinta basically put together a list of the materials we’d need to build this contraption and drew for us a quick diagram of what it would look like. This concluded most of our pre-action thoughts, but they certainly weren’t our last.

C. Process
The biggest, unexpected, challenge we faced in doing this project was definitely the creation of our field hockey module/contraption. We went to Home Depot and carefully selected all of the materials we’d need based off of Mr. Pinta’s suggestions. This included a PVC pipe, lots of wood, a dowel rod, bungee cords, and wood glue. We spent another day measuring and cleaning up our diagram so we knew exactly what the final product should look like. We faced some challenges with the wood glue and the nails in order to make sure everything was sturdy. We also had to play around with the bungee cords multiple times to ensure we knew what would be necessary to conduct a successful experiment later. Despite these difficulties, we were able to complete it and move on to do our experiments and get some data! However, before we actually took the contraption outside and test it, we were able to talk to the Stevenson JVA coach, Coach Wilcynski. We didn’t get to actually show her in person what we built, but she helped us a lot by re-teaching us in a bit more detail, the positioning and the best method to drive a ball. By watching her form and swing, we could tell that there indeed was an optimal angle at which she swung at to get the best drive. We already knew we couldn’t make up for the lack of power that our contraption would actually hit the ball with, but the swing would be the same. At an open field, we connected the 35” field hockey stick to the contraption and secured it with bungee cords (because we would need to reposition the stick different ways for different trials) Unfortunately, the day we chose to conduct our experiment happened to be very windy and cloudy so our biggest problem was that the PVC pipe kept moving as the stick swung down and missed the ball. We fixed this problem by having the person that’s not moving the stick,

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