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Fishing Rods Portfolio

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Introduction

International Baccalaureate

                    IB Math Standard Level

                                 Portfolio

                                   Type II

                              Fishing Rods

Sagar Sood

IB Math SL

Ms. Ridley

Due: 15th Oct, 09

Introduction

A fishing rod requires guides for the line so that it does not tangle and so that the line casts easily and efficiently.

In this investigation, a mathematical model will be developed that will calculate functions from the given data points of two fishing rods of lengths 230cm and 300cm. This model will further determine the placement of the line guides on the fishing rod.

In mathematics, a function is a relation between a given set of elements and another set of elements that associate with each other, algebraically and graphically. In this investigation, an approach using matrices will be attempted to calculate functions for the given data and then be plotted to verify the results. Furthermore, there will be an effective use of technology so as to minimize errors and flaws.

Variable

Let x= Guide number (from tip)

Let y= Distance from tip (cm)

...read more.

Middle

image08.png

Let image09.pngimage09.png be equal to image10.pngimage10.png

image11.pngimage11.png

image12.pngimage12.png

Hence, the equation is image14.pngimage14.png

The graph below shows the calculated quadratic equation that goes through the data points of Table 2

Figure 3

image15.pngimage15.pngimage16.png

This model is quite accurate as the curve of the function passes through all the points. Although the curve does not pass through the center of the data points on the graph.

One possible reason for flaw could be that only four data points were used to calculate the function, even though that was the only possibility. If there was a way to use all eight data points to calculate the function, the curve would go through all data points on the graph hence being more accurate.


image17.pngimage17.png

To calculate this equation, the first, third, sixth and eighth data points will be used.

Guide No. (from tip)

Distance from tip (cm)

1

10

3

38

6

96

8

149

Table 3

...read more.

Conclusion

image40.pngimage40.png

image41.pngimage41.png

image42.pngimage42.png

image43.pngimage43.png

image44.pngimage44.png

Adding a ninth guide to the rod would mean that the rod would be longer. The positive effect of adding a ninth guide to a longer rod would be that it would ensure that the line does not become tangled.

The table below shows the given set of data, which is Mark’s fishing rod that h as a 300cm line.

Table

Guide No. (from tip)

Distance from tip (cm)

1

10

2

22

3

34

4

48

5

64

6

81

7

102

8

124

The graph below shows the calculated quadratic function passing through the second set of data points (Mark’s fishing rod) from Table

image45.png

            It can be clearly seen that the quadratic function does not fit this new set of data. In order for that model to fit this new data, an enhanced quadratic would need to be recalculated using these new data points i.e. the same approach of matrices will be required. One limitation with this model is that it disregards the length of the fishing rod. A fishing rod with a different length would result in different data points. Different data points, would result in a new curve, which the original model does not fit.        

...read more.

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

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