# To Make An Unpredictable Move Biology Essay

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To make an unpredictable move before opponent can predict will gain you the advantage. In sports these unpredictable moves will lead to victory. Sometimes these things are known as techniques, some of these moves might be able to be explained by physics. Players may exploit the curvature to make the move and unpredictable, which leads them to victory. My research question is 'Does the amount of topspin affect the horizontal range of a ball'

Physics can explain these phenomena which to give advantage to the players, by understanding and employing them, players are able to exploit a tactical and physical advantage over their opponents. When thinking about the forces which act on balls or even anything around us, we can find that gravity, and Newton laws plays a big role. In sports these same principles apply to the ball which seems to follow a set path all the time. Upon looking closer we can see that these balls follow the motion in which most objects which are projected into the air will follow. In which players have learnt to gain a tactical advantage by using spin to alter the path of balls.

I would like to know if the application of topspin has an effect on the distance travelled, and if so what are the relationships maybe. As this allow additional knowledge to any ball sport game. Which eventually will lead to an advantage.

You haven't stated your research question in the Introduction. This is a MUST. See criterion A. +

Write down in the first paragraph exactly what your research question is. +

You need to discuss your own motivation for working on this topic further, Supavit. Think about why this subject is worthy of the time and effort you have put into it. See criterion B.

## BACKGROUND THEORIES

There will be forces which act on the ball when it still has motion in the air.

Gravity: This gives weight to the ball which has mass and thus falling back to the ground a 9.81 ms-2, this will help limit the amount of distance that the ball can travel.

## Newton's Laws:

Newton's first law states that everybody remains at rest or uniform motion unless it is exerted with an external unbalance force. Because of ball is constantly being affected by gravity as the external force, this causes the ball to eventually fall down to the ground, in which the ball follows the Projectile motion path.

Newton's third law states that for every action force there has to be an equal amount of reaction force acting against, so for the movement of the ball that has thrust in the forward direction there will be drag in the backwards direction, this then satisfies Newton's 3rd law.

## Air resistance:

Drag or air resistance is the force which goes against the thrust, or in this case it is the forward direction this is to satisfy Newton's 3rd law.

## Magnus Effect:

The Magnus effect is when, the spinning ball surface area is cutting through the air and the collisions with the passing air on one side of the ball causes the ball to decelerate which creates a high pressure area. While on the other side other side of the ball there is no collision which causes the air to move faster thus causing a low pressure area. And with the difference in pressure this creates the Magnus effect. The Magnus effect is therefore responsible for most of the curved motion of a spinning ball in sports.

This has an effect on the topspin, where in topspin it is used for sudden drop from the ball while it is still in air.

## Projectile motion:

Projectile motion is said to be how the motion of something moves in a parabolic motion when it is set of at an angle. In theory the object will reach a peak, and after that will fall with the same amount of distance that it has gained in the beginning. However in real life this does not happen, this is because of air resistance and gravity, which has an effect on the ball and thus only following the general shape of the projectile motion.

The projectile motion can be broken down into the x-component and the y-component, where the x-component is the distance that it has travelled, and the y-component is the height that the ball has reached. Both of the x-component and the y-component are acting at the same time; however they are independent of each other.

The vertical component of the projectile motion or the y-component, this is where gravity comes in which it accelerates the object down towards earth at 9.81ms-2; this is always changing 9.81ms-1 every second.

The horizontal component of the projectile motion or the x-component, this is the force which is acted onto the object, this is constant throughout the time in which it is following the projectile motion.

But for the purpose of this experiment only the x-component will be investigated since the research title is 'Does topspin affect the distance travelled by the ball?'

I don't think you really need this section Supavit, and it interrupts the flow of the essay. You can incorporate it into the body of the essay at appropriate places. For instance when you find yourself discuss thing the motion of the ball through the air, as discussion of air resistance, gravity and the Magnus effect would be appropriate. You have done good research to get the information above, so make sure you do include it, BUT you also need to make sure each piece of information above is appropriately referenced. At this stage a simple footnote like this

## Hypothesis:

The ball will travel less distance if there is topspin added to the ball, this is because of the Magnus effect, since the Magnus effect causes the curved path in most ball sports. And since the ball having more spin on the top, which causes the topspin to drop down towards the ground a lot faster than if it was hit normally. This is because of the buildup of low pressure at the top of the ball, which, because of this will have the faster velocity causing to spin and spread down; whilst near the bottom of the ball will have a high pressure, because of this it will have a lower velocity and thus dropping down at a much faster rate. The amount of spin that is exerted on the ball causes the ball to fall faster than if it is projected normally with a minimum amount of spin.

so therefore air resistance comes into play.

Which because of this by plotting all of the points into 1 graph, it will display a decrease in the distance, which will create a general trend for this hypothesis.

## DEVELOPMENT OF METHODOLOGY

Firstly for the preliminary experiments the ball was fired from the BOLA Bowling machine at 30 mph, was the default setting on the machine. Tape measures were placed down starting from 0 at the Bowling machine the maximum of 5 meters, after each shot from the machine, measurements would be taken by eye on the first bounce of the ball. By using this method, the amount of spin (RPM) could not be determined.

By removing the tape measure from the experiment and rely on the software logger pro, to analyze the data instead removes the human errors from the experiment. This was done by using a camera to video the motion of the ball until its first bounce. With this the x-component and y-component can be found.

To determine the exact amount of spin, the ball was painted with a red dot , this was to ensure that there was a minimum change in the surface area of the ball and this would allow the ball to rotate on its axis and time for how long it would take the ball to rotate frame by frame, and calculates it's revolution per minute. However when trying to capture the ball spinning, the camera could only capture a maximum of 30 frames per second, and this was not sufficient enough to determine the exact amount of spin that the ball was spinning with. Since the camera had to be set at a certain amount of space for it to be able to capture the whole displacement of the ball, it was unable to see the paint on the ball. To overcome this problem, the revolution per minutes was ignored and the settings on the BOLA bowling machine are used instead. This is because it is not possible to determine the exact amount of spin. And BOLA does not state the exact amount of spin which is used in the machine in the user manual nor can it be found using a search engine.

The setting on the machine was lowered to the minimum which is 15mph; this was to allow the camera to be able to capture the position of the ball which later logger pro can be used to analyze the video.

## VARIABLES

The independent variable in this experiment would be to change the amount of spin that is exerted on the ball; this would be done by selecting the pre-settings on the BOLA bowling machine

The BOLA Bowling machine consisted of Professional Bowling Machine which is used in delivering the balls, Power Pack, Leads, Practice balls all of these items are all BOLA products.

Changing the independent variable which will allow us to measure the dependent variable which is the distance travelled by the ball

The dependent variable that will be measured from this experiment will be the distance that it has travelled, from the machine. To get the dependent variable, a computer program, Logger Pro 3.6 will be used. With this program almost all of the information that will be needed can be obtained.

To keep the experiment as fair as possible these variables should be kept the same:

The type of ball which was used, under this category the ball should identically have the same amount of surface area, mass. This is to compensate for the huge amount of human error that can occur during the process of the experiment. But in reality this cannot be achieved so the balls that were used are assumed to be identical.

Force exerted on the ball - The speed exerted on the ball is kept at 15mph, this setting was used throughout the experiment, due to camera restraints of being able to take only 30fps. Even with this setting it is hard to use to logger pro to analyze the video, but still possible however a certain amount of error would be caused by the program itself. Also with the force of the ball, the angle at which the ball is projected with is kept the same.

There is loads of scope for expanding your discussion on control of variables, Supavit. You need to go into details because this is an extended piece of work.

## Apparatus:

BOLA Bowling machine

Computer with logger pro

Tape measure

Video camera

## Method:

Set up apparatus so that the video camera can capture the full flight of the ball.

Tilting the head of the BOLA machine so that it is perpendicular to the ground

Set the right bias on the BOLA machine to be the maximum (9)

Set the speed of the machine to be 15 mph

Start the video camera and insert the ball into the machine

After the ball has been fired, there is a waiting period before the next ball is placed in the machine, this is to get the speed of the machine back to the original setting

Decrease the right bias by 1 by clicking 'L' repeat until desired

Use Logger pro to analyze program

## LOGGER PRO:

Insert -&gt; Movie -&gt;[Drive]/ [File name]

Set scale by selecting the 'ruler' and setting a known distance in the program.

Click the position of the ball frame by frame.

This is the wrong format. You are writing an essay, not a science lab report. You need to incorporate your method into the main body of the essay in continuous prose, discussing why you chose this way of doing things, and difficulties you experienced and how you over came them in the process. You can include diagrams and photos of your work to enhance the discussion, and lend impact and precision you your points.

## CONCLUSION AND ANAYLYSIS

SPIN SETTING @ 9 LEFT 1500

SPIN SETTING @ 5 LEFT 1504

SPIN SETTING @ 1 LEFT 1508

X( VELOCITY)

X (meter)

X( VELOCITY)

X (meter)

X( VELOCITY)

X (meter)

0

0

0

0

0

0

1.17

0.31

0.39

0.11

1.22

0.17

2.22

0.86

0.75

0.48

2.27

0.59

2.57

1.4

0.94

0.93

2.64

1

2.66

1.96

0.99

1.38

2.76

1.44

2.42

2.52

1.04

1.83

2.72

1.85

1.74

3.06

1.03

2.29

2.7

2.27

1.04

3.47

0.02

2.72

1.99

2.38

SPIN SETTING @ 8 LEFT 1501

SPIN SETTING @ 4 LEFT 1505

SPIN SETTING @ NO SPIN 1509

X( VELOCITY)

X (meter)

X( VELOCITY)

X (meter)

X( VELOCITY)

X (meter)

0

0

0

0

0

0

1.48

0.2

0.94

0.3

0.75

0.4

2.88

0.67

1.76

0.73

1.51

0.83

3.44

1.11

2.08

1.14

1.88

1.26

3.57

1.58

2.27

1.6

2.01

1.69

3.37

2.05

2.2

2.04

2

2.12

2.65

2.43

1.94

2.45

1.97

1.45

1.83

2.72

1.44

2.59

SPIN SETTING @ 7 LEFT 1502

SPIN SETTING @ 3 LEFT 1506

X( VELOCITY)

X (meter)

X( VELOCITY)

X (meter)

0

0

0

0

1.17

0.28

1.76

0.19

2.26

0.73

3.3

0.66

2.63

1.19

3.77

1.13

2.66

1.65

3.92

1.58

2.47

2.11

3.91

2.06

2.01

2.53

3.53

2.52

1.27

2.69

3.01

2.78

SPIN SETTING @ 6 LEFT 1503

SPIN SETTING @ 2 LEFT 1507

X( VELOCITY)

X (meter)

X( VELOCITY)

X (meter)

0

0

0

0

0.89

0.07

1.13

0.15

1.72

0.33

2.24

0.58

2.01

0.78

2.75

1.05

2.14

1.24

2.86

1.54

2.3

1.7

2.79

2

2.42

2.16

2.59

2.48

0.09

2.51

2.31

2.89

## Conclusion:

From the collected data, my graph does not fit into with my hypothesis.

## Analysis:

The computer program that was used to analyze the videos is logger pro. This program enables us to find the x and y-components of the ball. After collected the data it will be transferred onto excel in order to find a relationship.

The anomalies on the graph are suspected to be caused by human error; this is because of the rapid increase and sudden decrease in the lines.

The sudden spike in graph 6 may have been caused by the lack of accuracy when it was being processed on logger pro, simply by miss clicking the 'correct' point on the program. This caused the ball to seem as if it has felt another external force being acted on the ball after it is in the air. However from another perspective assuming that there was no human error involved, this would mean that during that moment in time there was a change in the environment which has caused a higher wind speed which has affected the data. Also in addition to graph 6, the sudden drop in the distance travelled by the ball, this should have followed on the motion, and should have travelled a longer distance. There is reason to believe that the data points which were collected on the program were incomplete, which give would explain why the ball had travelled the least distance. This is because the ball that it is not the correct data point for that set of data.

The graph for no spin, does not seem to be valid, as it seems to be a stop half way, as if it did not fully go through all the projectile motion, as it does not satisfy the parabolic like shape. Instead it seems to have only been stopped half way. This may have been caused by the lower frame rate at which the movie is being videoed at, since it has only allowed some parts of the data to be collected.

The graphs which are produced by this set of results should have reached the ending point at the Y=0 axis, which if it does, this would make the graphs seem to be more valid to the hypothesis, this is because projected line would make the 'no spin' graph to have the most distance covered, and in between those would show that by adding topspin to the ball causes it to travel a smaller distance.

The graph does not show any relationship of any sort. This is because there is no order to the increase in distance, numerically instead it is all jumbled up. Seeing as in the BOLA manual group the amount of spin 1-3, 4-6 and 7-9 together, this suggest that if there was a trend then there had to be some links between those numbers, however since it is in no specific order a conclusion is drawn that there is no relationship.

A notice able error on the graph is when the ball travels to the maximum distance and it moves back. This error is caused during the analyzing process when the ball does seems to be as it is currently on the ground, however the next frame it is not. So because of this it causes the graph to seem as if the ball has moved back.

## Errors and uncertainties:

For the errors in measure the diameter of the ball I have used an error of ±0.5mm, this is because of the ruler that is used to measure the ball size is accurate up to 1mm, and therefore half the smallest digit for 1mm is 0.5mm. However the error in measuring the distance travelled by the ball is only ±0.5 cm, this was because half the smallest digit for a reasonable measurement, because a computer is used to process the data, they can be as accurate up to more than 6 significant number, upon trying to get a distance with the use of technology, the most accurate was up to 1cm, therefore half the smallest is ±5cm.

Calculating Percentage error: (Actual error / Experiment Error) x 100

Uncertainties in the equipment:

Ball

Actual error = 0.5mm

Percentage error = (0.5mm / 670mm) x 100

= ±0.07mm

= ±7 x 10-5m

Distance for spin 9

Actual error = 0.5cm

Point 1 ) Percentage error = (0.5cm / 0) x 100

= ±0

Point 2) Percentage error = ( 0.5cm/ (0.31 x 100) x 100

= ±1.61% error

Point 3) Percentage error = (0.5cm /0.86 x 100) x 100

= ±0.56% error

Point 4 ) Percentage error = (0.5cm /1.40 x 100) x 100

= ±0.35% error

Point 5 ) Percentage error = (0.5cm /1.96 x 100) x 100

= ±0.26 % error

Point 6 ) Percentage error = (0.5cm /2.52 x 100) x 100

= ±0.19 % error

Point 7 ) Percentage error = (0.5cm /3.06 x 100) x 100

= ±0.16% error

Point 8 ) Percentage error = (0.5cm /3.47 x 100) x 100

= ±0.14% error

From the graph that is produced, we can clearly see that the distance with spin clearly goes a lot further than the ball with spin. However there does not seem to any relationship according to these sets of results. Since there is no order in the graph, this has leaded me to believe that this experiment was filled with a lot of human error.

## EVALUATION

Overall through the experiment there is a lot of systematic due to the use of logger pro and random error which is caused by the setting of the experiment; which could have been reduced to improve the reliability of the results.

Additional raw data will help improve making an average of the data which was used, x meter and x velocity. Since by having addition

For example a section where the camera that is used could have been improved to be a high speed camera, as this would allow a much cleaner and more detailed video to be made, however it comes at the cost of needing a more powerful CPU to run the videos smoothly. With a improved camera, a more clearer frame by frame can be used, this will allow a lot more data points to be obtained, this is because of the smoothness that the logger pro can analyze to, so because of this the lager amount of data points can be plotted on the graph because of this it will have reduce both the systematic error and the random error in the experiment since, a better camera would mean that the precision of the data will become more precise. After having explored logger pro further, it is possible to plot the points while it is re-zeroed, this will reduce the amount of error whilst in the calculation process, as it helps reduce the amount of human error in the experiment since it is calculated in 1 go instead of having to manually re-zero the points, to allow easier comparison of the data points.

Using Logger pro for the data analysis could have been improved since; this is a powerful program to use, since it can calculate more than 6 significant digits thus being too accurate. However in this extended essay I have only set it to 3 significant numbers this is because, the scale on the ruler that was used to determine the distance which is used for comparing in logger pro, since the ruler is measured manually the significant number that can be used is half the smallest digit on the ruler. The smallest digit on the meter ruler is going up in 1 millimeter, so therefore we can only be as accurate to 0.5 of millimeter. This will only allow us to get as accurate as 4 significant numbers however, the reason which 3 significant figures is used is because, when using logger pro to analyze frame by frame the motion of the ball did not fully flow, and when it touches the ground it is not possible to determine the position of the ball to 4 significant numbers.

In addition to those, by changing the setting of experiment to be in a closed environment will allow reduce the amount in which the wind can affect on the projected ball. Because all of these data were collected in 1 day, they should be valid, however due to fact that during the course of the day outside factors may have little influence on the results.

Maybe by changing the method of collecting the data to a more traditional method, may have resulted into a more stable set of results, since by using technology, it is dependent on the input, which causes a lot of error during the process, simply by 'analyzing the data on the video', the amount accuracy is dependent on the eye, this amount is suspected to be the same as if the data is collected manually. This is because the computer screen is covered in pixels, we are not able to click to the exact pixel that we have previously clicked, and thus we are actually selecting out data points instead of measuring the same one.

In general this has a good deal of promise Supavit. You have given the impression in this first draft, that you conducted the experiment once, analysed the results once, and gave up when the data didn't fit your hypothesis. In reality I know that you repeated the experiment several times. Making improvements each time. This needs to be reflected in your essay. Try thinking of the essay as a timeline, and hang it together as such. Say what you did to start with, what worked and what didn't, what you changed and why, and then how the next time you did the experiment you developed more success.

A BIG limitation here is that you have tried to write this up as a lab report, when it is an essay. The two are very different. Irrespective of the content, 5 of the 11 grading criteria are simply assessing you have presented the essay in the correct way. I have added comments throughout the essay to help you restructure inline with what the IB have in mind. Before you go about doing this though, read carefully the grading criteria again.

The results you present and your evaluation of them is full of excuses for shortcomings in the analysis process. This is not excusable, since you have all the raw data you need to go back and re-analyse the work, and it is this process which the EE examiners are most interested in. See criteria C, D, E, F and K.

My current marks for you:

A: Research Question: 0

B: Introduction= 1/2

C: Investigation = 2/4

D: Knowledge and Understanding = 2/4

E: Reasoned Argument = ¼

F: Application of analytical and evaluative skills = 2/4

G: Language = ¼

H: Conclusion = ½

I: Formal presentation = ¼

J: Abstract = 0/2

K: Hollistic Judgement = 1/4

## APPENDIX

SPIN SETTING @ 9 LEFT 1500

FIRST BALL

## Y (VELOCITY

14.67

0.32

2.38

5.28

0.17

14.73

0.60

2.40

6.55

0.00

14.80

1.13

2.40

7.74

-0.32

14.87

1.69

2.37

8.21

-0.87

14.93

2.25

2.29

8.36

-1.60

15.00

2.82

2.15

8.18

-2.24

15.07

3.34

1.98

8.02

-2.76

15.13

3.87

1.76

8.00

-3.14

SECOND BALL

18.60

0.31

2.39

5.38

-0.05

18.67

0.59

2.39

6.72

-0.20

18.73

1.15

2.39

7.91

-0.57

18.80

1.71

2.33

8.25

-1.15

18.87

2.27

2.24

8.22

-1.80

18.93

2.83

2.08

7.77

-2.33

19.00

3.38

1.90

6.35

-2.43

19.07

3.61

1.75

4.78

-2.36

THIRD BALL

22.13

0.32

2.38

4.43

0.20

22.20

0.51

2.41

6.17

-0.06

22.27

1.08

2.39

7.65

-0.40

22.33

1.61

2.36

8.16

-0.88

22.40

2.18

2.28

8.48

-1.58

22.47

2.76

2.15

8.42

-2.25

22.53

3.31

1.98

8.25

-2.84

22.60

3.84

1.74

8.12

-3.26

FOURTH BALL

25.47

0.31

2.37

7.29

0.23

25.53

0.77

2.40

7.66

-0.04

25.60

1.32

2.39

7.97

-0.45

25.67

1.85

2.35

8.06

-1.10

25.73

2.40

2.25

8.00

-1.86

25.80

2.93

2.10

7.70

-2.46

25.87

3.48

1.89

6.76

-2.63

25.93

3.79

1.73

5.68

-2.54

SPIN SETTING @ 8 LEFT 1501

FIRST BALL

## Y (VELOCITY

9.87

0.30

2.25

4.62

-0.06

9.93

0.55

2.25

5.52

-0.21

10.00

1.00

2.24

6.31

-0.52

10.07

1.43

2.20

6.67

-1.09

10.13

1.90

2.10

6.72

-1.75

10.20

2.35

1.96

6.37

-2.27

10.27

2.82

1.76

5.16

-2.33

10.33

2.98

1.64

3.73

-2.12

SECOND BALL

14.67

0.28

2.23

3.35

0.03

14.73

0.43

2.25

4.75

-0.29

14.80

0.83

2.22

6.27

-0.69

14.87

1.33

2.17

7.00

-1.24

14.93

1.80

2.05

7.01

-1.78

15.00

2.27

1.93

6.70

-2.20

15.07

2.78

1.72

5.32

-2.15

15.13

2.93

1.63

3.68

-1.78

THIRD BALL

17.53

0.30

2.23

2.93

0.04

17.60

0.39

2.23

4.70

0.01

17.67

0.87

2.24

6.16

-0.22

17.73

1.29

2.23

6.60

-0.83

17.80

1.75

2.13

6.89

-1.55

17.87

2.22

2.01

6.83

-2.14

17.93

2.68

1.84

6.61

-2.54

18.00

3.09

1.65

6.38

-2.74

FOURTH BALL

19.60

0.31

2.26

2.36

-0.22

19.67

0.36

2.23

4.25

-0.11

19.73

0.79

2.25

6.05

-0.18

19.80

1.25

2.24

6.75

-0.67

19.87

1.72

2.18

6.94

-1.44

19.93

2.18

2.04

6.85

-2.00

20.00

2.63

1.90

6.80

-2.46

20.07

3.08

1.69

6.80

-2.89

SPIN SETTING @ 7 LEFT 1502

FIRST BALL

## Y (VELOCITY

12.33

0.34

2.25

5.87

-0.17

12.40

0.71

2.25

6.25

-0.42

12.47

1.14

2.22

6.74

-0.84

12.53

1.63

2.15

6.97

-1.43

12.60

2.09

2.04

6.91

-2.22

12.67

2.55

1.84

6.76

-2.78

12.73

2.98

1.63

6.58

-3.02

SECOND BALL

15.6

0.338466361

2.258534474

3.808019795

0.15838057

15.67

0.51

2.28

5.18

-0.03

15.73

0.97

2.28

6.41

-0.46

15.80

1.44

2.23

6.73

-1.05

15.87

1.88

2.14

6.80

-1.67

15.93

2.35

2.00

6.71

-2.22

16.00

2.81

1.83

6.23

-2.52

16.07

3.16

1.65

5.69

-2.66

THIRD BALL

18.47

0.34

2.27

3.51

-0.14

18.53

0.48

2.26

5.10

-0.22

18.60

0.96

2.25

6.49

-0.44

18.67

1.42

2.23

6.89

-0.99

18.73

1.90

2.13

6.84

-1.69

18.80

2.35

1.99

6.48

-2.19

18.87

2.78

1.82

5.87

-2.48

18.93

3.10

1.64

5.23

-2.64

FOURTH BALL

20.60

0.33

2.25

3.48

0.04

20.67

0.49

2.26

4.80

-0.14

20.73

0.91

2.26

6.06

-0.54

20.80

1.35

2.20

6.56

-1.14

20.87

1.80

2.10

6.72

-1.69

20.93

2.26

1.97

6.57

-2.13

21.00

2.71

1.80

5.98

-2.36

21.07

3.03

1.64

5.36

-2.45

SPIN SETTING @ 6 LEFT 1503

FIRST BALL

## Y (VELOCITY

9.20

0.36

2.29

4.43

0.04

9.27

0.60

2.30

5.46

-0.15

9.33

1.05

2.29

6.36

-0.47

9.40

1.50

2.25

6.66

-1.08

9.47

1.94

2.15

6.88

-1.72

9.53

2.40

2.03

7.24

-2.40

9.60

2.92

1.79

7.62

-3.03

SECOND BALL

11.93333333

0.37040709

2.288322566

4.845767283

0.007002554

12.00

0.64

2.30

5.77

-0.18

12.07

1.10

2.28

6.62

-0.48

12.13

1.57

2.25

6.85

-0.98

12.20

2.02

2.17

7.01

-1.78

12.27

2.50

2.00

7.20

-2.48

12.33

2.99

1.79

7.34

-2.90

THIRD BALL

15.00

0.36

2.31

2.67

-0.21

15.07

0.44

2.29

4.46

-0.12

15.13

0.87

2.31

6.15

-0.27

15.20

1.35

2.29

6.65

-0.89

15.27

1.78

2.20

6.80

-1.58

15.33

2.24

2.06

6.97

-2.04

15.40

2.72

1.93

7.01

-2.50

15.47

3.19

1.71

6.99

-2.93

FOURTH BALL

18.60

0.38

2.29

5.07

0.04

18.67

0.68

2.30

5.74

-0.14

18.73

1.10

2.30

6.48

-0.54

18.80

1.57

2.24

6.89

-1.12

18.87

2.04

2.15

7.00

-1.81

18.93

2.50

1.99

7.06

-2.46

19.00

2.98

1.78

7.12

-2.88

SPIN SETTING @ 5 LEFT 1504

FIRST BALL

## Y (VELOCITY

9.13

0.34

2.32

4.91

-0.07

9.20

0.63

2.32

5.59

-0.19

9.27

1.06

2.31

6.21

-0.41

9.33

1.48

2.29

6.55

-0.90

9.40

1.94

2.21

6.76

-1.67

9.47

2.40

2.06

6.62

-2.32

9.53

2.82

1.87

6.51

-2.58

9.60

3.26

1.70

6.47

-2.61

SECOND BALL

12

0.332773826

2.332466647

6.149142966

0.056478925

12.07

0.73

2.34

6.36

-0.11

12.13

1.17

2.34

6.55

-0.49

12.20

1.61

2.30

6.67

-1.16

12.27

2.07

2.19

6.61

-1.91

12.33

2.48

2.03

6.60

-2.39

12.40

2.99

1.85

6.05

-2.59

12.47

3.28

1.67

5.16

-2.65

THIRD BALL

14.73

0.34

2.31

5.76

0.10

14.80

0.70

2.32

6.25

-0.18

14.87

1.15

2.32

6.67

-0.68

14.93

1.61

2.25

6.80

-1.37

15.00

2.07

2.12

6.81

-1.91

15.07

2.50

1.99

7.02

-2.33

15.13

3.01

1.79

7.33

-2.67

FOURTH BALL

17.07

0.34

2.31

6.38

-0.13

17.13

0.76

2.31

6.57

-0.37

17.20

1.21

2.28

6.77

-0.78

17.27

1.66

2.22

6.95

-1.45

17.33

2.15

2.09

6.96

-2.10

17.40

2.58

1.93

7.13

-2.65

17.47

3.09

1.71

7.44

-3.10

SPIN SETTING @ 4 LEFT 1505

FIRST BALL

## Y (VELOCITY

8.27

0.36

2.33

2.90

-0.06

8.33

0.47

2.32

4.49

-0.05

8.40

0.90

2.33

5.94

-0.15

8.47

1.33

2.33

6.48

-0.64

8.53

1.77

2.26

6.81

-1.30

8.60

2.25

2.15

6.82

-1.90

8.67

2.69

2.00

6.76

-2.48

8.73

3.14

1.79

6.80

-2.89

SECOND BALL

11.13333333

0.364015716

2.315938556

4.660347599

0.134161522

11.20

0.61

2.33

5.75

-0.07

11.27

1.09

2.32

6.68

-0.39

11.33

1.56

2.30

6.86

-0.96

11.40

2.01

2.21

6.92

-1.69

11.47

2.49

2.07

6.77

-2.32

11.53

2.94

1.88

6.25

-2.67

11.60

3.30

1.69

5.75

-2.78

THIRD BALL

14.07

0.37

2.32

4.98

-0.11

14.13

0.66

2.32

5.74

-0.20

14.20

1.11

2.32

6.42

-0.54

14.27

1.54

2.27

6.77

-1.27

14.33

2.02

2.15

7.03

-1.92

14.40

2.50

2.00

6.99

-2.37

14.47

2.95

1.81

6.87

-2.70

FOURTH BALL

17.13

0.37

2.31

4.96

0.45

17.20

0.69

2.35

5.25

0.13

17.27

1.07

2.37

5.47

-0.47

17.33

1.41

2.29

5.69

-1.14

17.40

1.83

2.21

5.81

-1.72

17.47

2.20

2.07

5.71

-2.35

17.53

2.61

1.87

5.36

-2.62

17.60

2.91

1.70

4.88

-2.63

SPIN SETTING @ 3 LEFT 1506

FIRST BALL

## Y (VELOCITY

8.60

0.50

2.41

2.20

-0.01

8.67

0.53

2.41

4.29

-0.11

8.73

0.99

2.42

6.17

-0.42

8.80

1.44

2.38

6.92

-1.03

8.87

1.94

2.28

7.23

-1.66

8.93

2.41

2.16

7.21

-2.28

9.00

2.92

1.96

6.92

-2.65

9.07

3.33

1.78

6.51

-2.75

SECOND BALL

11.2

0.501546256

2.428777742

3.601313122

-0.094199337

11.27

0.65

2.43

5.20

-0.24

11.33

1.13

2.41

6.64

-0.52

11.40

1.61

2.37

7.07

-0.93

11.47

2.10

2.31

7.00

-1.63

11.53

2.54

2.16

6.90

-2.39

11.60

3.04

1.95

6.55

-2.69

11.67

3.41

1.78

6.00

-2.70

THIRD BALL

14.13

0.48

2.42

3.48

-0.07

14.20

0.61

2.42

5.13

-0.20

14.27

1.13

2.40

6.38

-0.42

14.33

1.55

2.39

6.53

-1.04

14.40

1.98

2.28

6.77

-1.89

14.47

2.46

2.12

6.80

-2.37

14.53

2.96

1.94

5.93

-2.55

14.60

3.21

1.77

4.81

-2.60

FOURTH BALL

16.60

0.49

2.43

3.04

-0.03

16.67

0.60

2.43

4.75

-0.13

16.73

1.05

2.43

6.34

-0.39

16.80

1.53

2.39

6.86

-0.91

16.87

1.99

2.32

7.00

-1.58

16.93

2.46

2.19

7.03

-2.26

17.00

2.93

2.00

7.04

-2.76

17.07

3.40

1.79

7.04

-3.07

SPIN SETTING @ 2 LEFT 1507

FIRST BALL

## Y (VELOCITY

8.27

0.54

2.42

3.14

-0.24

8.33

0.66

2.39

4.60

-0.18

8.40

1.07

2.42

6.08

-0.43

8.47

1.54

2.36

6.82

-1.10

8.53

2.02

2.26

6.98

-1.70

8.60

2.47

2.13

6.98

-2.18

8.67

2.96

1.96

6.85

-2.50

8.73

3.38

1.78

6.59

-2.64

SECOND BALL

10.53

0.53

2.41

3.48

0.00

10.60

0.68

2.41

4.92

-0.08

10.67

1.10

2.42

6.44

-0.36

10.73

1.60

2.38

7.14

-0.94

10.80

2.10

2.30

7.07

-1.64

10.87

2.54

2.17

6.99

-2.32

10.93

3.03

1.96

6.98

-2.64

11.00

3.47

1.79

6.85

-2.67

THIRD BALL

13.00

0.53

2.39

3.61

0.06

13.07

0.69

2.39

4.96

0.02

13.13

1.13

2.42

6.22

-0.30

13.20

1.57

2.38

6.82

-0.99

13.27

2.05

2.29

7.16

-1.78

13.33

2.55

2.12

7.02

-2.24

13.40

3.00

1.97

6.71

-2.41

13.47

3.42

1.80

6.49

-2.52

FOURTH BALL

15.27

0.54

2.40

3.71

-0.01

15.33

0.70

2.41

5.15

-0.21

15.40

1.16

2.38

6.43

-0.47

15.47

1.62

2.36

6.90

-1.00

15.53

2.10

2.26

7.02

-1.73

15.60

2.56

2.13

6.91

-2.39

15.67

3.06

1.91

6.35

-2.60

15.73

3.39

1.76

5.60

-2.44

SPIN SETTING @ 1 LEFT 1508

FIRST BALL

## Y (VELOCITY

9.07

0.55

2.42

3.19

0.42

9.13

0.72

2.44

3.86

0.50

9.20

1.04

2.51

4.39

0.33

9.27

1.35

2.51

4.41

-0.22

9.33

1.63

2.48

4.31

-0.89

9.40

1.90

2.41

4.43

-1.78

9.47

2.23

2.23

4.49

-2.45

9.53

2.53

2.07

4.20

-2.99

9.6

2.77

1.81

3.89

-3.49

SECOND BALL

11.87

0.55

2.40

1.93

-0.01

11.93

0.55

2.40

4.14

-0.11

12.00

1.02

2.41

6.02

-0.43

12.07

1.45

2.36

6.70

-0.96

12.13

1.94

2.29

7.02

-1.61

12.20

2.39

2.14

6.99

-2.22

12.27

2.87

1.97

6.98

-2.51

12.33

3.32

1.79

6.91

-2.66

THIRD BALL

14.53

0.55

2.42

3.89

-0.15

14.60

0.73

2.41

5.25

-0.25

14.67

1.20

2.40

6.45

-0.51

14.73

1.65

2.36

6.87

-1.12

14.80

2.13

2.25

7.05

-1.78

14.87

2.60

2.12

6.99

-2.41

14.93

3.06

1.90

6.92

-2.95

FOURTH BALL

17.33

0.56

2.40

5.21

-0.25

17.40

0.87

2.39

5.88

-0.49

17.47

1.32

2.36

6.47

-0.94

17.53

1.75

2.28

6.83

-1.59

17.60

2.25

2.15

6.91

-2.18

17.67

2.69

1.98

6.73

-2.64

17.73

3.13

1.77

6.64

-2.92

SPIN SETTING @ NO SPIN 1509

FIRST BALL

8.13

0.54

2.40

5.70

-0.18

8.20

0.89

2.39

6.30

-0.32

8.27

1.36

2.37

6.83

-0.62

8.33

1.82

2.34

7.12

-1.31

8.40

2.31

2.20

7.38

-2.06

8.47

2.81

2.05

7.51

-2.58

8.53

3.32

1.83

7.59

-2.97

SECOND BALL

11.53

0.55

2.40

6.21

-0.24

11.60

0.95

2.39

6.57

-0.45

11.67

1.40

2.36

6.96

-0.85

11.73

1.88

2.30

7.27

-1.50

11.80

2.40

2.17

7.29

-2.19

11.87

2.87

1.99

7.05

-2.63

11.93

3.32

1.79

6.87

-2.86

THIRD BALL

14.93

0.55

2.39

3.39

-0.04

15.00

0.70

2.40

4.81

-0.31

15.07

1.12

2.37

6.25

-0.73

15.13

1.59

2.32

6.87

-1.43

15.20

2.06

2.18

7.15

-2.03

15.27

2.55

2.05

7.25

-2.56

15.33

3.03

1.81

7.26

-3.07

FOURTH BALL

17.73

0.55

2.40

2.45

0.74

17.80

0.68

2.44

3.08

0.75

17.87

0.92

2.52

3.76

0.51

17.93

1.22

2.54

4.03

-0.08

18.00

1.48

2.51

3.96

-0.78

18.07

1.73

2.43

3.97

-1.52

18.13

2.02

2.31

3.91

-2.23

18.20

2.25

2.12

3.93

-2.77

18.27

2.53

1.91

4.09

-3.07

## Calculations.

Distance for spin 9

Actual error = 0.5cm

Point 1 ) Percentage error = (0.5cm / 0) x 100

= ±0

Point 2) Percentage error = ( 0.5cm/ (0.31 x 100)) x 100

= ±1.61% error

Point 3) Percentage error = (0.5cm /(0.86 x 100)) x 100

= ±0.56% error

Point 4 ) Percentage error = (0.5cm /(1.40 x 100)) x 100

= ±0.35% error

Point 5 ) Percentage error = (0.5cm /(1.96 x 100)) x 100

= ±0.26 % error

Point 6 ) Percentage error = (0.5cm /(2.52 x 100)) x 100

= ±0.19 % error

Point 7 ) Percentage error = (0.5cm /(3.06 x 100)) x 100

= ±0.16% error

Point 8 ) Percentage error = (0.5cm /(3.47 x 100)) x 100

= ±0.14% error

Distance for spin 8

Actual error = 0.5cm

Point 1 ) Percentage error = (0.5cm / 0) x 100

= ±0

Point 2) Percentage error = ( 0.5cm/ ((0.20 x 100)) x 100

= ±2.5% error

Point 3) Percentage error = (0.5cm /(0.67 x 100)) x 100

= ±0.75% error

Point 4 ) Percentage error = (0.5cm /(1.11 x 100)) x 100

= ±0.45% error

Point 5 ) Percentage error = (0.5cm /(1.58 x 100)) x 100

= ±0.31 % error

Point 6 ) Percentage error = (0.5cm /(2.05 x 100))x 100

= ±0.25 % error

Point 7 ) Percentage error = (0.5cm /(2.43 x 100)) x 100

= ±0.2.0% error

Point 8 ) Percentage error = (0.5cm /(2.72 x 100)) x 100

= ±0.18% error

Distance for spin 7

Actual error = 0.5cm

Point 1 ) Percentage error = (0.5cm / 0) x 100

= ±0

Point 2) Percentage error = ( 0.5cm/ (0.28 x 100)) x 100

= ±1.78% error

Point 3) Percentage error = (0.5cm /(0.73 x 100)) x 100

= ±0.68% error

Point 4 ) Percentage error = (0.5cm /(1.19 x 100)) x 100

= ±0.42% error

Point 5 ) Percentage error = (0.5cm /(1.65 x 100)) x 100

= ±0.26 % error

Point 6 ) Percentage error = (0.5cm /(2.11 x 100)) x 100

= ±0.23 % error

Point 7 ) Percentage error = (0.5cm /(2.53 x 100)) x 100

= ±0.19% error

Point 8 ) Percentage error = (0.5cm /(2.69 x 100)) x 100

= ±0.19% error

Distance for spin 6

Actual error = 0.5cm

Point 1 ) Percentage error = (0.5cm / 0) x 100

= ±0

Point 2) Percentage error = ( 0.5cm/ ((0.07 x 100)) x 100

= ±7.14% error

Point 3) Percentage error = (0.5cm /(0.33 x 100)) x 100

= ±1.15% error

Point 4 ) Percentage error = (0.5cm /(0.78 x 100)) x 100

= ±0.64% error

Point 5 ) Percentage error = (0.5cm /(1.24 x 100)) x 100

= ±0.4 % error

Point 6 ) Percentage error = (0.5cm /(1.70 x 100)) x 100

= ±0.29 % error

Point 7 ) Percentage error = (0.5cm /(2.16 x 100)) x 100

= ±0.23% error

Point 8 ) Percentage error = (0.5cm /(2.51 x 100)) x 100

= ±0.20% error

Distance for spin 5

Actual error = 0.5cm

Point 1 ) Percentage error = (0.5cm / 0) x 100

= ±0

Point 2) Percentage error = ( 0.5cm/ (0.11 x 100)) x 100

= ±4.54% error

Point 3) Percentage error = (0.5cm /(0.48 x 100)) x 100

= ±1.04% error

Point 4 ) Percentage error = (0.5cm /(0.93 x 100)) x 100

= ±0.53% error

Point 5 ) Percentage error = (0.5cm /(1.38 x 100)) x 100

= ±0.36 % error

Point 6 ) Percentage error = (0.5cm /(1.83 x 100)) x 100

= ±0.27 % error

Point 7 ) Percentage error = (0.5cm /(2.29 x 100)) x 100

= ±0.21% error

Point 8 ) Percentage error = (0.5cm /(2.72 x 100)) x 100

= ±0.18% error

Distance for spin 4

Actual error = 0.5cm

Point 1 ) Percentage error = (0.5cm / 0) x 100

= ±0

Point 2) Percentage error = ( 0.5cm/ (0.30 x 100)) x 100

= ±1.66% error

Point 3) Percentage error = (0.5cm /(0.73 x 100)) x 100

= ±0.68% error

Point 4 ) Percentage error = (0.5cm /(1.14 x 100)) x 100

= ±0.43% error

Point 5 ) Percentage error = (0.5cm /(1.6 x 100)) x 100

= ±0.3.1 % error

Point 6 ) Percentage error = (0.5cm /(2.04 x 100)) x 100

= ±0.24 % error

Point 7 ) Percentage error = (0.5cm /(2.45 x 100)) x 100

= ±0.20% error

Point 8 ) Percentage error = (0.5cm /(2.59 x 100)) x 100

= ±0.19% error

Distance for spin 3

Actual error = 0.5cm

Point 1 ) Percentage error = (0.5cm / 0) x 100

= ±0

Point 2) Percentage error = ( 0.5cm/ (0.19 x 100)) x 100

= ±2.63 % error

Point 3) Percentage error = (0.5cm /(0.66 x 100)) x 100

= ±0.75% error

Point 4 ) Percentage error = (0.5cm /(1.13 x 100)) x 100

= ±0.44% error

Point 5 ) Percentage error = (0.5cm /(1.58 x 100)) x 100

= ±0.31 % error

Point 6 ) Percentage error = (0.5cm /(2.06 x 100)) x 100

= ±0.24 % error

Point 7 ) Percentage error = (0.5cm /(2.52 x 100)) x 100

= ±0.19% error

Point 8 ) Percentage error = (0.5cm /(2.78 x 100)) x 100

= ±0.18% error

Distance for spin 2

Actual error = 0.5cm

Point 1 ) Percentage error = (0.5cm / 0) x 100

= ±0

Point 2) Percentage error = ( 0.5cm/ (0.15 x 100)) x 100

= ±3.33% error

Point 3) Percentage error = (0.5cm /(0.58 x 100)) x 100

= ±0.86% error

Point 4 ) Percentage error = (0.5cm /(1.05 x 100)) x 100

= ±0.47% error

Point 5 ) Percentage error = (0.5cm /(1.54 x 100)) x 100

= ±0.32 % error

Point 6 ) Percentage error = (0.5cm /(2.00 x 100)) x 100

= ±0.25 % error

Point 7 ) Percentage error = (0.5cm /(2.48 x 100)) x 100

= ±0.16% error

Point 8 ) Percentage error = (0.5cm /(2.89 x 100)) x 100

= ±0.17% error

Distance for spin 1

Actual error = 0.5cm

Point 1 ) Percentage error = (0.5cm / 0) x 100

= ±0

Point 2) Percentage error = ( 0.5cm/ (0.17 x 100) x 100

= ±2.94% error

Point 3) Percentage error = (0.5cm /0.59 x 100) x 100

= ±0.84% error

Point 4 ) Percentage error = (0.5cm /1.00 x 100) x 100

= ±0.5% error

Point 5 ) Percentage error = (0.5cm /1.44 x 100) x 100

= ±0.34 % error

Point 6 ) Percentage error = (0.5cm /1.85 x 100) x 100

= ±0.27 % error

Point 7 ) Percentage error = (0.5cm /2.27 x 100) x 100

= ±0.22% error

Point 8 ) Percentage error = (0.5cm /2.38 x 100) x 100

= ±0.21% error

Distance for no spin

Actual error = 0.5cm

Point 1 ) Percentage error = (0.5cm / 0) x 100

= ±0

Point 2) Percentage error = ( 0.5cm/ (0.40 x 100)) x 100

= ±1.25% error

Point 3) Percentage error = (0.5cm /(0.83 x 100)) x 100

= ±0.60% error

Point 4 ) Percentage error = (0.5cm /(1.26 x 100)) x 100

= ±0.39% error

Point 5 ) Percentage error = (0.5cm /(1.69 x 100)) x 100

= ±0.29 % error

Point 6 ) Percentage error = (0.5cm /(2.12 x 100)) x 100

= ±0.23 % error

Point 7 ) Percentage error = (0.5cm /(1.45 x 100)) x 100

= ±0.34% error

The appendix is very hard to follow and need more information to give the reader an appreciation of what all these numbers mean. This would be helped if you had discussed the analysis for the video footage you recorded in Logger Pro within the main body of the essay.