Reference no: EM131191425

MATH-240 - Calculus Project - Play Ball

To be successful on your project you must:

-Read and follow instructions carefully.

-Review the grading rubric carefully to ensure you are familiar with the expectations for each section.

-If you need clarification about any part of this project, please be sure you ask your instructor in a timely manner.

-Ten percent will be deducted for each calendar day the project is submitted after the due date. A project is considered as "submitted" when it is available to the professor to view in Canvas.  No credit is given after five days late (two days late during summer and winter terms). 

-After you submit your project please open it up in Canvas to ensure it is readable.

-Write clearly, using appropriate terminology and accurate mathematical notation.   College-level writing is expected, as is the use of correct grammar.

• If you need help with writing, feel free to use the HCC Writing Center: For further information, see the HCC Web page under the heading "Writing Center" or call the Writing Center at (443) 518-4101. PGCC students at the Laurel College Center should see the PGCC Writing Center for assistance.

-Submit a neat, professional report as a PDF file.  You may create the project using your choice of word processing software.  It should be double-spaced, use a mathematical notation package, and include printouts and diagrams from your choice of graphing application, computer algebra software, and/or statistical software (as applicable). The use of appropriate technology is expected throughout the project. 

• In particular, embedded "complete" graphs or charts and/or computer printouts will be expected as part of the report. Hand-drawn graphs are not acceptable.
• Hand calculations (if applicable to the project requirements) should be scanned and included as an appendix at the end of the report.

-For this project group work will not be allowed. While you may get ideas from others, each student must submit their own project. 

-Original work is expected.  This means that students who are repeating the course are expected to create an entirely new project using different functions.  TurnItIn will be used as a deterrent to plagiarism.

-Getting help:  You may ask questions of others but your work must be your own and you must write up your own documents to be turned in.

• For this project, you may consult any resource (including your instructor, tutors (LAC, HR230), classmates, or the Internet) for general help and advice provided that your write-up (computations, explanations, and embedded diagrams) are your own work.
• For example, you might watch a YouTube video on how to do a regression or have a peer show you how to make a complete graph using a different dataset (not the one in your project), then try it yourself with your data. You might consult your textbook or your instructor about a concept, but then put the explanation into your own words.

-Submission guidelines:

• You should submit your project via the Canvas link as a PDF file.
• TurnItIn will be used as a deterrent to plagiarism. This program is integrated into the Canvas submission process. All submissions will be compared against the TurnItIn database and receive an "originality" rating. To avoid a false flag in TurnItIn, do not copy and paste the instructions/questions into your final submission.
• To earn the maximum score on this project, it is expected that students go "above and beyond" the minimum expectations of the project.

Calculus Project - Play Ball

The project is about vectors, motion in space, and curvature/tangent/normal vectors.

The goal of this project is twofold.  First, the student must demonstrate competency in MATLAB programming, producing an "m" file with commands to perform the calculus and generate the graphs required for the project.  Second, the student must produce a report describing their project and their results.

Much ado has been made in baseball over the concept of the speed of a pitch.  More recently some attention has been diverted to the concept of "exit velocity," the speed of the baseball after contact with the bat.  See the following article in the New York Times:

https://www.nytimes.com/2015/05/05/sports/baseball/baseballs-latest-craze-its-like-rocket-science.html?_r=0

Here are two more links where you can find information about exit velocity.

https://www.hardballtimes.com/improving-projections-with-exit-velocity/

https://docs.google.com/spreadsheets/d/1AN7wQLndx3TemuiWLdbrBoGwEdmAUG_EZY1J9BQLe5s/edit?pref=2&pli=1#gid=35651174

In this project you will explore the concept of exit velocity as applied to hitting in baseball.  The same concept could be applied to a tennis ball, a golf ball, a cricket ball, a racquetball, etc.  It could also be applied to balls that are thrown rather than hit, such as basketball or a football, or it could be applied to balls that are kicked, such as soccer balls and footballs. 

You are to pretend that you are an engineer working for a sporting goods firm.  You have done research and have developed a new material for a baseball bat that will give a ball 10% more exit velocity than a traditional bat.  You are to write a report to your supervisor with appropriate citations.  Be sure to explain the concept of exit velocity in your report.

For this project you need to find information about the exit velocity of current bats.  You will then select a major league baseball park (your choice) and will need the distance from home plate straight out to the center field fence (the distance needed for a ball to be a home run).  Be sure to determine the height of the fence, as balls bouncing off the fence below that height will not be home runs.

Ignore effects of players jumping to catch balls hit near the top of the fence.  Be sure to account for the height of the ball when it leaves the bat.

One link to information about baseball fields is the following.

https://espn.go.com/fantasy/baseball/story/_/page/mlbdk2k16_parkfactors/which-parks-most-least-favorable-fantasy-baseball-hitters-pitchers-mlb#ARI links to info on 30 major league baseball parks

You will be using a coordinate system set up so that the origin is at home plate, with the y-axis extending out to center field and the z-axis pointing directly upward.

You will need to use MATLAB to compute the range of angles over which a baseball, hit with a current typical exit velocity, will be a home run.  Use whole numbers for the degree measure of your angles.  Your MATLAB program should also compute the horizontal distance (to the nearest foot) the ball will travel (y-max) for various angles.

https://m.mlb.com/glossary/statcast/launch-angle Launch angle for various results of hitting a baseball.  

Angle guidelines are given.

Your MATLAB program should graph the trajectory, as seen in the y-z plane, of the angle that clears the fence by the largest amount.  Your report should include the vector equation for the trajectory.  Use MATLAB to compute the curvature, the unit tangent vector, and the unit normal vector at the moment the ball clears the fence.

You will then repeat this process using an exit speed that is 10% higher than the current speed, corresponding to use of a baseball bat made using your new material - produce a table and a graph.

Be sure to discuss the "impact" your bat might have on the game of baseball.

Your report should include all of the information you used in this project, any tables and figures you wish to include (which should be able to be reproducible using your m file), a description of the trajectories and the differences between the trajectories due to the two different bat materials, and your conclusions.  Be sure to upload your report as a PDF file (Word can "save as").  Upload your M file as is so that it can be run by your instructor.

Additional resources:

https://www.hittrackeronline.com/howitworks.php Home Run Tracker

https://www.beabetterhitter.com/baseball-bat-sweet-spot/ good article Timing + accuracy = POWER!