Throwing a rubber ball at a CBR
1. The following data was obtained by throwing a rubber ball at a CBR.
|
Time (sec)
|
Height (m)
|
|
0.0000
|
1.03754
|
|
0.1080
|
1.40205
|
|
0.2150
|
1.63806
|
|
0.3225
|
1.77412
|
|
0.4300
|
1.80392
|
|
0.5375
|
1.71522
|
|
0.6450
|
1.50942
|
|
0.7525
|
1.21410
|
|
0.8600
|
0.83173
|
a) Use the data above to make a scatterplot, letting xrepresent the number of seconds elapsed.
b) Next, use a graphing calculator to find the model that best expresses the height and vertical velocity of the rubber ball. We can also use this model to predict the maximum height of the ball and its vertical velocity when it hits the face of the CBR.
c) Fit linear, quadratic, cubic, and power functions to the data. By comparing the values of, determine the function that best fits the data.
d) Graph the function of best fit with the scatterplot of the data.
e) Determine the maximum height of the ball (in meters).
With the model you selected in part (b), predict when the height of the ball is at least 1.5 meters.