Bouncing
Ball
(this is the work of Lee Nguyen)
(this is the work of Lee Nguyen)
Materials: A tennis ball, a ruler, and firm floor.
Procedure: Drop the tennis ball from different heigth and record the bouncing height for different dropping height. Investigate the relationship bewteen the drop height and the bounce height.
Data Set: I made a table of data in EXCEL:
Scatter Plot: A scatter plot in EXCEL
Analysis of Data:
I noticed from the data that the ball always bounce off to a same
percentage of each dropping height. Here is a calculation which
I tabulated on my calculator which shows that the ratio of the
bouncing height to the dropping height remain relatively constant
within acceptable expiremental error for each different dropping
height.
L1=dropping height,
L2=bouncing height, L3= L2/L1
Notice thatthe ratio L3=L2/L1
doesn't signigficantly changes from from one pair of data point
to another. Thus, I suspect that L1 and L2 are possibly linearly
related. Then, I performed a linear regression on my calculator.
Below is the result:
As it turns out, L1 and L2 do exhibit a linear relationship because of the coefficient of correlation r is 1. Thus, the algrebriac model for this relationship between the dropping height and bouncing height is
y=.46(x) + .03, where x=dropping height and y= boucing height.
Prediction: So if I dropped a ball off the top of Shaquille O'Neal's head (he is 7'1" wich equals 215.9cm) I would expect the ball to bounce up 99.344cm or about 3'3".
I calculated this prediction by evaluating the linear model when x = 215.9cm
Extension: We might extend this problem to finding
the relationship between the succesive bouncing heights to its
previous heights.
