In this activity, students will use the calculator's differential equation graphing mode to model projectile motion. They analyze time-height data for a falling object using the statistical features of the calculator. They also compare the data with the theoretical equations. They will also model baseball trajectories with and without air resistance.

Before the Activity

Drop a book from a height of 0.8649 meters and measure its height above the ground at different time intervals using the CBL 2™ unit

Examine and visualize the data

See the attached PDF file for detailed instructions for this activity

Print pages 35 - 44 from the attached PDF file for your class

During the Activity

Distribute the pages to the class.

Follow the Activity procedures:
Modeling the Motion of Falling Objects with Scatter Plots and Differential Equations

Understand the relationship between the variables in the data

Enter the time and height data as list

Set up a scatter plot and graph the data

Determine the differential equation for falling objects (theoretical model for falling objects)

Compare the solution to the equation with the scatter plot

Observe that the solution to the differential equation matches the plot well though it diverges toward the end of the plot

Find a curve of best fit for the scatter plot

Compare the equation of the best-fit curve (regression curve) with the analytic solution of the differential equation

Modeling Baseball Trajectories

Use the differential equation mode and enter the system of equations that represent the motion of a baseball

Graph the solution and find the distance traveled by the ball

Modeling Baseball Trajectories with Air Resistance

Use the given value for deceleration due to air resistance and determine the distance traveled by the baseball

After the Activity

Review student results:

As a class, discuss questions that appeared to be more challenging