IB Student

DP1 HL Mathematics

Internal Assessment Type II

## My Internal Assessment

In this internal assessment, I am going to create a recursive formula for a mathematic model. In this investigation, I use real life examples and uses real data to finish my investigation. Afterward, I place my model to real life case study. However, there are different limitations in different cases. Some of the limitations are dimensional plane, speed, boundaries and more. At last, I am going to present my recursive formula, .

The speed of Ada and Fay

After reading the Internal Assessment question sheet, I had an idea on using a similar real life case study. Then, I invite my cousin, Ada and her dog, Fay, to have a running test and let me collect a set of data for my Internal Assessment. Therefore, I set a straight track with a distance of 100 meters and they need to run for 10 times. So, I can collect a set of accurate data. After each of them run for 10 times, I will take an average time for the 100 meters run and then uses the speed formula, . In this formula, V stands for velocity, which is the speed; the S stands for distance, at last, T stands for the period of time the runner runs. Below is Ada’s data for running 100 meters:

Ada’s running records

After collecting Ada’s set of data, then I need to define the average time of Ada running a 100 meters track, in the other word, the mean of the data. Therefore, I am going to use the mean equation from the statistic chapter, which is. The calculation will be as follow,

From the calculation, I define that the average time of Ada running 100 meters is 16.7 seconds. Furthermore, after finding the time of Ada running 100 meters, I need to define the speed Ada runs in the experiment. To find the velocity, I will apply an equation that I use both in Physic and in Mathematic, which is . Therefore, by plugging the “s” and “t” values, then the result of the calculation will be the velocity. The calculation will be as follow,

After calculation, I found that the velocity of Ada is 5.988 m/s. Due to further easier calculation; I decide to round up Ada’s speed to one significant figure. Therefore, her speed for running 100 meters is 6.0 m/s. Moreover, after defining the speed of Ada, it is time to investigate Fay’s velocity of running 100 meters. The method of finding Fay’s velocity is same as finding Ada’s velocity. Below there will be table presenting Fay’s record of running 100 meters for 10 trails.

Fay’s running records

Then, I am going to define the average velocity of Fay’s running time by using the mean formula.

After finding Fay’s average time, which is 12.5 seconds. Then, I am going to define the speed of Fay’s runs, by the speed formula. The calculation will be as follow,

After the calculation, the outcome of Fay’s running velocity is 8 m/s. Therefore, now I had define the velocity of Ada’s running speed and Fay’s speed. Furthermore, I am going to use the information I got above to construct a diagram out, which simulates the situation.

Diagram involve both runner position and direction

In this diagram, there will be direction indicate where the runner is running and how they run in actual situation. Furthermore, I also set Ada’s velocity as “u m/s” and Fay’s velocity is “v m/s”. Ada is running in a straight line along the harbor path using the velocity of 6 m/s and Fay is using 8m/s running towards Ada, which its direction will change due to Ada’s position. Therefore, “u” will appear on the Y-axis and “v” will be on the X-axis.