2D Projectile Motion
Summary
In this class activity, we will solve for the motion of an object in more than one dimension. Because motion along each axis is independent, we treat this problem as two separate numerical calculations in 1 dimension, one in the x direction and one in the y direction. For this problem, we assume that acceleration only occurs along the y-axis perpendicular to the earth's surface.
In this activity, students will learn how to employ the Euler method to study the two-dimensional motion of a kicked ball. This is a problem that they have studied using pen and paper. Here, they will see how the same problem can be approached numerically and can eventually be used to study more complex problems in which pen and paper would not be convenient.
Keywords: Projectile problem, 2-D motion, Euler method
CollapseLearning Goals
Students will learn how to employ the Euler method for numerical integrating a differential equation to solve a very familiar general physics problem.
Context for Use
This activity is suitable for second-year students, who have taken introductory physics in a small classroom setting in a primary undergraduate institute. Students are able to complete this in class in a one-hour time period.
Students need basic knowledge of MATLAB, using live scripts, and know how to work with vectors, arrays, and for-loops. They should know how to plot their results.
Description and Teaching Materials
Student Handout for the class activity (Microsoft Word 2007 (.docx) 17kB Oct12 23)
The teaching material is in the form of an instructive step-by-step guided worksheet, which they complete on the lab day in the computer lab. It is built on the introductory physics concepts and introductory programming skills they gained in the previous weeks. This activity will prepare the students for the next stage, which is a time-dependent acceleration.
Teaching Notes and Tips
The students are expected to Transfer the worksheet into a LiveScript code. The worksheet asks individual questions, which should be answered and discussed. They are supposed to include their codes, plots, and answers in their Livescript and submit the Livescript code and a PDF version of it. The submitted PDF should be such that the instructor or the TA can easily assess the work without needing to open the original LiveScript code in MATLAB.
Assessment
1) The PDF version of the Livescript should be clear and understandable as a stand-alone item. 2) The plots and the results should be clear and will be graded based on the correctness of the results. 3) Each question and discussion will be assessed separately.