Homerun Parabolas
By Shannon Kephart
This week, students in the Advanced Algebra and Trigonometry classes applied their knowledge of the quadratic equation to investigate the parabolic shape of a homerun ball. Students watched a video of Boston Red Sox player David Ortiz hitting a homerun during the 2013 World Series. The famous “Green Monster”, the 37-foot-tall left-field wall of Fenway Park in Boston, often presents an obstacle to a homerun, but Ortiz launched the baseball over the wall and out of the park with one, quick swing. Students began a discussion about the measurements of different parks and speculated why Fenway Park has such a tall left-field wall. Perhaps, students predicted, the left-field wall is there to make it harder to hit a homerun in Fenway, or to make it more difficult for right-handed hitters.
Using Desmos.com, an online graphing tool, students plotted three quadratic equations that are possible trajectories of a baseball hit from home plate. A homerun often seems effortless when it’s seen soaring to heights over the outfield walls. However, students discovered that homeruns are more complicated than they look. Hits by baseball players vary widely in height and distance, as students discovered by finding the vertex, x-intercepts, and y-intercepts. When transferring their online graph to a diagram of a baseball field, it was tricky to figure out how a negative number might be incorporated into the trajectories, or how to determine if a ball hit in a certain park would result in a homerun. Of the three hits plotted, students discovered that only one would be a homerun in Fenway Park.
Then, students looked at the equation for the trajectory of an average homerun and at the measurements of hometown ballparks Wrigley Field and U.S. Cellular Field. Comparing the distance to and the height of left-field walls in each of these parks, students used the average homerun equation to determine if the average homerun would make it out of the outfield of either park. Next week, students will determine in which park it is easier to hit a home run, providing new fuel for arguing who is the better team!
This tasked was adapted from a task available on Mathalicious.com.