A bowling ball is set into motion on a smooth level surface, and data were collected for the total distance covered by the ball at each of four times. These data are shown in the table in Problem 66 . Your job is to learn to use a spreadsheet program $-$ for example, Microsoft Excel-to create a mathematical model of the bowling ball motion data shown. You are to find what you think is the best value for the slope, $m$, and the $y$ -intercept, $b$. Practicing with a tutorial worksheet entitled MODTUT.XLS will help you to learn about the process of modeling for a linear relationship. Ask your instructor where to find this tutorial worksheet.
After using the tutorial, you can create a model for the bowling ball data given above. To do this:
(a) Open a new worksheet and enter a title for your bowling ball graph.
(b) Set the $y$ -label to Distance $(m)$ and the $x$ -label to Time $(s)$.
(c) Refer to the data table above. Enter the measured times for the bowling ball in the Time $(s)$ column (formerly $x$ -label).
(d) Set the $y$ -exp column to $D$ -data $(m)$ and enter the measured distances for the bowling ball (probably something like $0.00 \mathrm{~m}, 2.00$ $\mathrm{m}, 4.00 \mathrm{~m}$, and $6.00 \mathrm{~m} .$ ).
(e) Place the symbol $m$ (for slope) in the cell B1. Place the symbol $b$ (for $y$ -intercept) in cell $\mathrm{B}$ 2.
(f) Set the $y$ -theory column to D-model $(\mathrm{m})$ and then put the appropriate equation for a straight line of the form Distance = $\mathrm{m}^{*}$ Time $+\mathrm{b}$ in cells $\mathrm{C} 7$ through $\mathrm{C} 12$. Be sure to refer to cells $\mathrm{Cl}$ for slope and $C 2$ for $y$ -intercept as absolutes; that is, use $\$ C \$ 1$ and $\$ C \$ 2$ when referring to them.
(g) Use the spreadsheet graphing feature to create a graph of the data in the D-exp and D-theory columns as a function of the data in the Time column.
(h) Change the values in cells $\mathrm{Cl}$ and $\mathrm{C} 2$ until your theoretical line matches as closely as possible your red experimental data points in the graph window.
(i) Discuss the meaning of the slope of a graph of distance vs. time. What does it tell you about the motion of the bowling ball?