Math IA

Topics: Length, Distance, Real number Pages: 7 (499 words) Published: November 19, 2013
IB Math Studies Internal Assessment:
Is the distance a tennis ball travels horizontally dependent on the angle of which it is dropped at?

Exam Session: May 2014
School Name:
Teacher:
Course: IB Math Studies
Word Count: 654
Name:

Is the distance a tennis ball travels horizontally dependent on the angle of which it is dropped at? Introduction
In tennis, players hit the tennis ball in certain ways so the ball goes the way they want it to go. Hitting it at certain angles enables the tennis ball to travel various distances, it depending on the angle. Some angles make the ball go short or far distances. Statement of Task

The main purpose of this investigation is to determine whether there is a relationship between the distance a tennis ball travels horizontally and the angles of which it is dropped at. The type of data that will be collected is that I will drop a tennis ball, at a constant height of 4 feet, at from different angles (30°, 40°, 50°, 60°, 70°), twenty times for each angle with a total of one-hundred drops and measuring the distance of each drop in feet. The data will be used to determine whether the angle of which a ball is dropped affects how far a tennis ball travels horizontally.

Plan of Investigation
I am investigating if the distance a tennis ball travels horizontally dependent on the angle it is drops at. I have collected data on the distances a tennis ball travels horizontally at five various angles (30°, 40°, 50°, 60°, 70°). With the collection of data that I have acquired, a number of mathematical processes were used to analyze the data: scatter plot, histogram, and linear regression. Diagram of the set-up of investigation

Mathematical Investigation
Collected Data

Angles of which tennis ball were dropped at

Trails
30°
40°
50°
60°
70°

1
11.23
10.45
9.65
8.62
7.32

2
11.47
10.23
9.81
8.18
7.41

3
11.56
10.56
8.13
8.32
7.18

4
12.26
10.23
9.21
7.47
6.97

5
11.27
10.18
9.71
8.90
7.53

6
11.31
9.95
9.34
8.21
7.57

7
11.48
10.65
9.09
9.25
7.21

8
10.96
10.59
10.12
8.84
8.01

9
11.12
11.07
9.91
8.65
7.74

10
11.48
10.29
9.52
9.52
7.18

11
11.56
10.34
8.89
8.04
6.89

12
11.69
10.77
9.27
8.11
7.11

13
12.05
9.88
9.80
7.32
7.87

14
11.36
10.84
9.76
8.79
7.43

15
11.17
10.97
10.15
8.18
7.31

16
11.25
10.43
9.57
8.36
6.91

17
10.86
11.11
9.41
8.48
7.65

18
11.40
10.08
9.23
7.97
8.10

19
11.92
10.31
8.97
8.56
7.72

20
11.76
10.49
9.81
8.91
7.25
Table 1: The horizontal distances the tennis ball traveled from various angles

This table shows all of the distances the tennis ball traveled at five equal intervals of angles. The tennis ball was dropped twenty times for each angles, total drops of one-hundred.

Calculation of the average distances for each angle
Average of a set is found by adding all the numbers in the set and dividing by the total number of the set. Ex: Average distance of 30° 11.23+11.47+11.56+12.26+11.27+11.31+11.48+10.96+11.12+11.48+11.56+11.69+12.05+11.36+11.17+11.25+10.86+11.40+11.92+11.76=229.003 Average distance (feet) the tennis ball traveled horizontally for each angle 30°

40°
50°
60°
70°
11.45 ft.
10.47 ft.
9.47 ft.
8.43 ft.
7.42 ft.
299.003÷20=11.45

Average distance (feet) the tennis ball traveled horizontally for each angle

This graph is a scatter graph of the average distances (feet) the tennis ball traveled horizontally for each angle.

Histogram of average distance (feet) the tennis ball traveled horizontally for each angle

Conclusion
After processing the data, it can be seen that the distance a tennis ball travels horizontally is dependent on the angle at which it is dropped. The ball went farther at 30° than it did at any other angle. The average distance for each angle was at equal...

Cited: Picture on cover:
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