Education Technology

# Activities

• ##### Subject Area

• Math: Precalculus: Parametric Equations

College

60 Minutes

• ##### Device
• TI-89 / TI-89 Titanium
• TI-92 Plus / Voyage™ 200

#### Activity Overview

In this activity, students find the time a man takes to catch a moving train. They solve the problem with and without using calculus.

#### Before the Activity

• See the attached PDF file for detailed instructions for this activity
• Print pages 1 - 2 from the attached PDF file for the class
• #### During the Activity

Distribute the pages to the class.

Without Calculus:

• Examine the graph which shows the distances as a function of time if a man runs at constant velocity
• Find the two points where the person can catch the train
• Solve the system for any speed and find two solutions for time
• Find the minimum speed to catch the train for which the two values for time are equal

• Using Calculus:
• Understand that the man is moving at minimum velocity and that the train has the same speed when he catches it
• Find the position of the train door at a certain time and find the speed of the train at that time
• Calculate the speed of the man running behind the train

• Alternatively, find the equation of the tangent line as a first order Taylor polynomial
• Solve the system for time
• #### After the Activity

Review student results.

• As a class, discuss questions that appeared to be more challenging
• Re-teach concepts as necessary