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.
Follow the Activity procedures:
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