Trajectory Notes

The Trajectory Interactive is an adjustable-size file that displays nicely on smart phones, on tablets such as the iPad, on Chromebooks, and on laptops and desktops. The size of the Interactive can be scaled to fit the device that it is displayed on. The compatibility with smart phones, iPads, other tablets, and Chromebooks make it a perfect tool for use in a 1:1 classroom.

This Interactive is intended for use near the later stages of a learning cycle on projectile motion. The Interactive is essentially a spreadsheet program. Input parameters are provided and the program calculates the output parameters as a function of time. The Input Parameters are defined in the program itself. But more detailed information is provided on our Parameters Page here on the website. The output parameters include x- and y-components of position, velocity, acceleration, and air resistance as a function of time. These values can be viewed in a tabular and graphical format. There are two data screens with seven output variables each and 9 options for graphs. The graphical format relies upon the Plotly Javascript Graphing Library. Use of this library provides great looking plots. But more importantly, the plots are interactive, allowing the user to mouse over points and view values for the data. We've included some handy buttons allowing users to easily toggle between vthe nine graph options.

We recognize that some classrooms who use the program will have already had a unit of study on Newton's Laws and others have not. The two Data screens will accommodate each group. The first data screen includes strictly kinematic quantities - times, positions, velocities, and accelerations. The second data screens includes quanties that will be of interest to those analyzing the motion from a Newton's laws perspective. The graphical displays of air resistance in the x- and y-direction as a function of time also provide some rich discussion points for teachers.

The Interactive allows a user to explore a question. Users can quickly navigate between the Input Parameters screen, the Data View, and the Graphical View and back by clicking buttons found at the top of the page. The intent of the Interactive was to encourage students and classrooms to develop a testable question centered around a realistic scenario and to use the program to investigate the question. Towards that end, we have provided an activity sheet that provides some structure for such an investigation without damping the creativity. The activity sheet is available in PDF format with rights to use with your classrooms. We've also provided the source document for the activity (.docx) for download. Teachers are encouraged to modify it for use with their own classes. A rubric is included with the activity to facilitate feedback and grading.

Our calculation engine has a set of constraints associated with it. These are described in detail on our Parameters Page. Some of these constraints are due to how we perform calculations of the output parameters. Others are associated with the assumptions that we have made about air resistance. We have assumed that the force of air resistance is proportional to the square of speed. While this is a commonplace assumption, it is not exactly accurate for all objects - particularly low speed and low mass objects.

The most important input parameter is the time increment (∆time). This is the time interval over which we repeat our caclulations during the fall. We discuss this in detail on our Parameters Page. If you are using this activity with your classroom, emphasize the mportance of a good time increment. If it is too small, the program takes some time to calculate all the date (especially for tall initial heights). And it ∆time is too large, the calculated data lacks accuracy (especially for low initial heights and high initial speeds.

The value of g is a variable in the program. This allows for field trips to the moon and other planets ... without administrative approval. How cool is that! For those students who wish to compare an air resistance scenario to a no-air resistance scenario, the air density can be set to 0 for the purely free-falling situation.

Finally, we did not dress the provided activity up as such, but we believe a true NGSS activity can be made from this Interactive. For those who take the lead in doing so, we would be delighted to view what you have created.