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The Physics Professor and the Water Balloon

Your college physics professor walks past your second story dorm room window every day after school. For reasons completely unknown, you decide that you would like to hit her with a water balloon after the last day of class. To avoid the embarrassing situation of missing, you throw several practice shots. From this, you can make a scatter plot and a linear regression line to determine exactly how fast you need to throw the balloon for it to hit your professor.

Your window is on the second story of the building, and the sidewalk is 3 meters away from the building.

Question Group #1
Directions and/or Common Information: 

First, you must make your scatter plot. The data to be entered is shown below in Fig. I.1.

VhRange
3.5 m/s 2.5 m
3.75 m/s 2.7 m
4 m/s 2.9 m
4.25 m/s 3.1 m
4.5 m/s 3.2 m

Fig. I.1

To do this, press , then select 1: Edit...  If there is any data in either column L1 or L2, select the column name and hit clear and then the down arrow. Neither column should have any data. (Fig. I.2).


Fig. I.2

Now type in each value of Vh into L1. Remember to press enter between each. Press the right arrow to go to L2, and type in each value for Range, again pressing enter between each. You should now have 5 entries in each column (Fig. I.3).   

 
Fig. I.3  

To get the scatter plot to show up, you must press , choose a scatter plot (the first icon) as your graph. The data to be used is in L1 and L2. 


Fig. I.4

Now adjust your window to fit the data. Use Xmin=3  Xmax=5 Xscl=1  Ymin=2  Ymax=4 Yscl= 1 (Fig. I.5).


Fig. I.5

Now press .  Your screen should now look like Fig. I.6


Fig. I.6



1. 




Question Group #2
Directions and/or Common Information: 

The next task is to make a linear regression line in order to find the exact speed at which to throw the balloon. To do this, press , select the CALC menu, and select item 4: LinReg(ax+b) (Fig. II.1),


Fig. II.1

then press enter twice (Fig. II.2).


Fig. II.2

If your calculator does not display "r" or "r2," you can press 2nd then 0 to go to the catalog, and select the item "Diagnostic On" and press enter twice. Now repeat the first step.

"r" and "r2" are used to determine how well the line fits the data. "r2 " is simply "r" multiplied by itself and is always between 0 and 1. "r" can be any value between -1 and 1. An "r" value of -1 or 1 means you have a perfect fit. As "r" values get closer to 0, the less correlation there is in your data.

Now press , and clear all the equations. Go to Y1 and press , select item 5: Statistics...  Go to the EQ menu, and select item 1: RegEQ and press enter (Fig. II.3).


Fig. II.3

The equation should now appear in the Y1 (Fig. II.4).


Fig. II.4

Now, press , and you should see the regression line appear over top of the points (Fig. II.5).


Fig. II.5

To find when this line equals 3, you will have to press again, and type 3 into the Y2. Then use the technique learned in "Police and Neon" to find the intersection of the two lines. The x value of this intersection is the speed at which the ball would need to be thrown (Fig. II.6).


Fig. II.6



1. 




Question Group #3
Directions and/or Common Information: 

A few of your friends have seen you making your practice throws, and have decided they would like to collaborate with you. They are located on the first and third stories of the dorm building. Their data is shown below in Fig. III.1 and Fig III.2. 

VhRange
2 m/s 2.4 m
2.25 m/s 2.7 m
2.5 m/s 3.1 m
2.75 m/s 3.3 m
3 m/s 3.6 m

Fig. III.1
VhRange
13 m/s 2.6 m
14 m/s 2.8 m
15 m/s 3.1 m
16 m/s 3.2 m
17 m/s 3.4 m

Fig. III.2



Use the techniques learned above to find the speed each of them needs to throw their balloon.
1. 








J Burch

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