Yr 11 MATHS B

ASSIGNMENT

Task one

The aim of this assignment was to determine and create the most suitable

and efficient Whirlybird which could sustain flight times the longest. The

method followed to achieve this was a series of flight test. Different

sizes of Whirly birds were created in 2cm intervals in the length and the

width. Then each model will be dropped from the same height keeping all

variables the same, six times and recording the flight time to the ground.

The recorded flight times will be analysed and used to determine the best

Whirlybird. It will be analysed using different mathematical methods and

graphs to provide suggestions. The process taken to complete the experiment

followed the method explicitly. The recording of the whirlybird drops were

unaffected by natural elements such as the weather because it was kept

indoor in a controlled environment (wind resistance and hight control were

not a problem). The timing using a stop watch was kept by the same person

so reaction time would not defer while recording. When transferring the

data to a computer for analysis, the means and standard deviation were

calculated for each of the six drops of each whirlybird and put into datal

plots. The data plots were used to break down the information and put into

TI Interactive. It would then use it aid in the analysis process by

plotting graphs and calculating a regression.

Task 2

Lengths cm |1ts |2nd |3rd |4th |5th |6th |mean |SD | |2 |1.42 |1.78 |2.03

|2.08 |1.6 |1.42 |1.7217 |0.291 | |4 |2.82 |1.87 |3.07 |3.16 |2.55 |2.86

|2.7217 |0.4684 | |6 |3.72 |3.6 |3.51 |4.37 |4.05 |3.69 |3.8234 |0.3246 |

|8 |4.3 |4.96 |6.01 |4.64 |4.93 |4.95 |4.756 |0.2876 | |10 |5.56 |5.38

|4.66 |4.89 |4.82 |4.77 |5.0134 |0.36604 | |12 |3.76 |3.87 |3.57 |4.03

|3.02 |3.74 |3.655 |0.3506 | |14 |1.92 |1.89 |2.3 |2.48 |3.42 |3.25 |2.8625

|0.5548 | |16 |2.01 |2.32 |2.35 |1.81 |1.98 |2.12 |2.0984 |0.2088 | |

The data above is all the information gathered during the wing length

flight tests, it was used during the experiment for the analysis process.

It consists of the six drops for each whirly bird and the mean and standard

deviation of each set. The Mean and standard deviation were calculated to

easily identify the best length for a whirlybird. The data marked in RED

were selected as the out riders they were taken out of the calculation to

ensure the results were ordinary and not unique for the information.

Task 3

The data below is the graphical representation of the results recorded

during the flight test for the best length of a whirly bird. TI Interactive

was used because of it ability to produced the most accurate and reliable

results for finding the quadratic regression and line of best fit for the

graph. The graph bellow was chosen because it depicts the movements of the

data accurately along the graph.

picpic

pic

(9.16379, 4.55496) Maximum

Task 4

A separate investigation was set up to the determine the best width for the

whirlybirds wings. It followed the same process and method as the first

experiment. Except for the fact that the width length would only be between

one and three cm. It had the same six drops for each of the three

whirlybirds and was recorded under the same conditions as the first

experiment, it was then recorded and the same calculations were made before

transferring the data onto a computer. It was then analysed and the

following were created using TI Interactive quadratic regression, a

graphical display and data table.

Task 5

Width cm |1st |2nd |3rd |4th |5th |6th |mean |SD | |1 |2.01 |2.32 |2.35

|1.81 |1.98 |2.12 |2.0983 |0.2088 | |2 |1.8 |2.19 |2.08 |2.28 |1.89 |2.11

|2.048 |0.2009 | |3 |2.7 |5.22 |5.76 |4.68 |2.7 |7.09 |4.6917 |1.7381 | |

The data above is all the information gathered during the wing Width flight

tests; it was used during the experiment for the analysis process. It

consists of the six drops for each whirly bird and the mean and standard

deviation of each set. The Mean and standard deviation were calculated to

easily identify the best Width for a whirlybird. The data marked in RED

were selected as the out riders they were taken out of the calculation to

ensure the results were ordinary and not unique for the information.

Task 6

The data below is the graphical representation of the results recorded

during the flight test for the best width of a whirly bird. TI Interactive

was