Education Technology

# Activities

• ##### Subject Area

• Maths: Calculus: Applications of the Derivative

9-12

60 Minutes

• TI-86

CBL™/CBL 2™

• ##### Other Materials
This is Activity 4 from the EXPLORATIONS Book:
Differential Equations With The TI-86

## Projectile Motion

#### Activity Overview

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
• Re-teach concepts as necessary