Estimation and Limits -- Tangents -- Discovery

The graph below shows data collected when we dropped a pillow on a range-finding device. The table below the graph shows the same data. This data is also available in the CAS window that you opened when you entered this module. You can work through this module using this data or you can collect your own data using the TI-CBL.

Time  Height 

0.00     4.18803
0.02     4.18083
0.04     4.17722
0.06     4.15202
0.08     4.11241

0.10     4.07639
0.12     4.02958
0.14     3.96836
0.16     3.89634
0.18     3.81352

0.20     3.71629
0.22     3.61186
0.24     3.49662
0.26     3.36699
0.28     3.23015

0.30     3.0897
0.32     2.94566
0.34     2.77281
0.36     2.60716
0.38     2.43071

0.40     2.24706
0.42     2.0526
0.44     1.85454
0.46     1.64928
0.48     1.44762

• Find the velocity of the pillow at the time t = 0.20

• The data above came from from measurements made of the height of a pillow as it fell. They might, just as well, have been measurements made of a curved piece of metal at various points. Think of them in this way and find the slope of the tangent to this curve at the point t = 0.20

The figure below shows the tangent that we seek (in red).

You can work on these problems in your CAS window.

After you have solved the two problems above to your satisfaction go on to the reference section of this module.