# Projectile Motion and Circular Motion

## Summary

4 MATLAB Grader (previously Cody Coursework) problems assigned to freshmen physics majors in a general physics course are described. The physics concepts are projectile motion and circular motion.

## Learning Goals

Upon completing this activity, students should be able to convert a problem that is typically solved analytically to a computational problem using a MATLAB function or script. Students will learn to program a function and/or script and evaluate it for different parameters using MATLAB and verify their analytical calculations.

Specifically, students will learn to (a) fill in a template for a function or script to represent equations, (b) correctly use variables to evaluate the function or script for the problem, and (c) produce the correct calculation for the problem using a MATLAB function or script.

## Context for Use

The MATLAB Grader problems were developed for a freshman physics course on the concepts of circular motion and projectile motion. Throughout the semester, 3 or 4 MATLAB Grader problems are assigned along with 7 or 8 homework problems on the same concepts from the chapter of the textbook to be completed with paper and pencil. The addition of the computational problems provides students with the opportunity to develop their computational skills to program MATLAB functions and scripts to verify their analytical calculations.

Students have completed Matlab Onramp and 3 similar assignments on the topics of kinematics and vectors in MATLAB Grader before this assignment.

## Description and Teaching Materials

The files included in this activity are screenshots of the 4 problems in MATLAB Grader. Students are expected to replace the question marks with variables and to successfully evaluate the MATLAB function or script.

## Teaching Notes and Tips

The expectation is that students have little to no programming experience before using MATLAB Grader. Before assigning MATLAB Grader problems, students are assigned MATLAB Onramp. To teach students to use MATLAB Grader, the instructor provides example problems and works through the analytical problems first. Then, the instructor explains and gives examples of functions and scripts and how they differ. Finally, the instructor walks students through the completion of the template for a function and a script for the analytical problems and also the evaluation of the function and script. The instructor explains the test code used in the MATLAB Grader assessment and shows the student solutions provided to the instructor.

## Assessment

The MATLAB Grader system tests student solutions for completion and correctness. In addition to the parameters given in the problem, the system also tests the student solutions with random numbers to prevent students from using constants instead of parameters in the functions.

Two examples of correct and incorrect student solutions are provided. The first example shows the solutions of the same student for the problem titled, Circular Motion 1. In the incorrect solution, constants were used inside the function. While this evaluates correctly for this problem, when the function is evaluated with random numbers by the MATLAB Grader system, it evaluates incorrectly. The student corrected their solution and received full credit. Settings in MATLAB Grader provide options for the number of attempts allowed.

The second example shows solutions for two different students for the problem titled, Projectile Motion. In the incorrect solution, the student's equation for the time is incorrect. The correct solution of another student is provided for comparison.