Meet Me Where?

Suppose two people walking meet on the street and pass each other. These motions can be modeled graphically. The motion graphs are linear if each person is walking at a constant rate.

In this activity, you will investigate modeling the motion of these two people to find where they will meet and at what rate each was walking.

For each group you will need:

  • 2 CBR units
  • 2 TI-83/84 Family Graphing Calculators

Each group should be made up of 2 walkers and 2 holders.

Instructions:

  1. Find the EasyData program on the calculators (Under Apps).
  2. Enter the setup instructions on both calculators.

a.Select the soft key Setup

b. Select the first option, 1: Dist. Then press .

c. Once in the Sensor Setup screen, change the units to ft, by pressing the soft key Units . Then press . Then soft key OK

d.Select the soft key Start

e.Select the soft key OK. This will start the data collection (Refer to

running the experiment). The walker needs to start walking when the

CBR2 starts fast ticking. The ticking will stop automatically after 5

seconds

Running the experiment

Both holders should stand at one end of the “course.” Walker A needs to start on the same end at the holders and Walker B should be about 12 feet away facing the holders and Walker A.

Holder 1 Walker A

Holder 2Walker B

Data Collection

1.The graph for Walker A should be a line with positive slope. The result for Walker B should be a line with negative slope. If you are not satisfied with the results of your experiment, select

soft key Main and try again.

2.When you are satisfied with you data, sketch a Distance-Time plot for each walker. Thegraph will appear on the screen.

3. You will need both sets of data to answer the following questions.

Questions

1. Use to determine the coordinates of the starting distance for

each walker as Point 1. Using trace to one other point on each of the

distance graphs for each walker. Record this point as Point 2.

Point 1 / Point 2
Time / Distance / Time / Distance
Walker A
Walker B

2.The velocity of each walker is the change in distance,, divided by the change

in time, . Find the velocity for each walker.

/ / velocity =
Walker A
Walker B

3.What are the units associated with the velocity? ______

4.Slope is defined to be the rate of change. What would determine the rate of

change of the distance for each walker?

______

5.Find the slope and the y-intercept of each line. Write the equation of the line that best fits the

Distance-Time graph for each walker.

m / b / Equation of Line
Walker A
Walker B

6.What is the physical significance of the y-intercept for each walker?

______

______

7.The slope of the line for Walker A is positive, while the slope of the line for Walker B is negative. Explain the significance of the sign of each walker’s slope.

______

______

______

8.Press WINDOW. Change the Xmin to 0 and the Xmax to 5

Ymin to 0 and the Ymax to 15. Press Y=. Enter the equation

of the line for Walker A in Y1. Enter the equation for Walker

B in Y2. PressGRAPH.Record a sketch of the graphs of the

two walkers.

9.To find the point of intersection, press CALC (2nd [Trace]). Select 5:INTERSECT. Press ENTER ENTER ENTER. Record this point.

Point of Intersection: ______

10.What is the significance of the y-coordinate of the point of intersection of these two graphs?

______

______

11.What is the significance of the x-coordinate of the point of intersection of these two graphs?

______

______