# How Far Can You Throw (or Kick) a Ball?

 Areas of Science Sports Science Difficulty Time Required Average (6-10 days) Prerequisites None Material Availability This science project requires a computer with internet access and a digital video camera with a tripod. See the Materials and Equipment list for details. Cost Low ($20 -$50) Safety Be sure to do this science project in an open area like an empty football field, where you will not hit people or buildings with the ball.

## Abstract

Have you ever seen a "Hail Mary" football pass, where the quarterback tries to throw the ball as far as possible to reach the end zone and score a touchdown? Or a last second game tying soccer goal from midfield? How far the ball will go does not just depend on how hard a player throws or kicks it; it also depends on the angle at which the player launches the ball. In this sports science project, you will investigate how launch angle affects the distance that a ball travels by filming volunteers who throw (or kick) a ball and analyze the videos with a motion-tracking software tool.

Note: This science project is written using football as the example, but you could do the project for any sport that involves throwing or kicking a ball.

## Objective

Throw (or kick) a football at different launch angles and measure which one results in the longest horizontal distance using a free motion-tracking software program.

## Credits

Ben Finio, PhD, Science Buddies
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• Excel® is a registered trademark of Microsoft Corporation.

General citation information is provided here. Be sure to check the formatting, including capitalization, for the method you are using and update your citation, as needed.

### MLA Style

Science Buddies Staff. "How Far Can You Throw (or Kick) a Ball?" Science Buddies, 23 June 2020, https://www.sciencebuddies.org/science-fair-projects/project-ideas/Sports_p036/sports-science/how-far-can-you-throw-or-kick-a-ball?from=Blog. Accessed 24 Oct. 2020.

### APA Style

Science Buddies Staff. (2020, June 23). How Far Can You Throw (or Kick) a Ball? Retrieved from https://www.sciencebuddies.org/science-fair-projects/project-ideas/Sports_p036/sports-science/how-far-can-you-throw-or-kick-a-ball?from=Blog

Last edit date: 2020-06-23

## Introduction

Note: This science project is written with throwing a football as an example, but you can adapt this project to work with any sport where you throw or kick a ball. The only exception would be if the ball is too small to easily see on a camera from a distance, like a golf ball.

You might not think that a football game and your science class have anything in common. But if you watch football, you know that the football is often launched through the air; it can be thrown, kicked, or punted (see Figure 1). Any object that is launched through the air is called a projectile. A football, a cannonball, a rock fired out of a slingshot, or a crumpled up wad of paper you throw across the room are all examples of projectiles.

The study of how projectiles move through the air is called projectile motion. As the projectile moves, it is affected by the forces of gravity and air resistance. When there is zero air resistance, a projectile moves in a path called a parabola. When there is air resistance (which always happens here, due to Earth's atmosphere, but would not happen somewhere like the Moon, where there is no atmosphere), a projectile does not move in a perfect parabola, but its path is still very close to one.

Figure 1. A football quarterback has to understand projectile motion in order to accurately throw the ball to a receiver (photo courtesy of U.S. Navy).

Understanding projectile motion can be very important in a game like football, where, depending on the play, you might need to throw a ball into the end zone, kick it through the field goal posts, or punt it high into the air. In this science project, you will focus on the best way to throw the ball as far as possible, like for a game-winning touchdown play.

The horizontal distance a projectile travels before it hits the ground (or, more simply, how far the ball will go when you throw it) is called its range. The range of a projectile depends on three things: its initial speed, its launch angle, and the initial height above the ground. Initial speed is how fast the ball is going the moment it leaves the quarterback's hand. If you throw the ball harder, it will have a higher initial speed. Launch angle is the angle the ball is traveling relative to the ground right when it is thrown. A launch angle of 0° means a ball is thrown straight out, parallel to the ground. A launch angle of 90° means a ball is thrown straight up, perpendicular to the ground. The initial height is the distance between the ball and the ground, the moment it leaves the thrower's hand. Figure 2, illustrates range, initial speed, launch angle, and initial height.

Figure 2. The range, initial speed, launch angle, and initial height of a projectile.

Can you think about how initial speed, launch angle, and initial height will affect the range of a projectile? The relationship between initial speed and range might seem obvious—if you throw a ball harder, it will go farther. There is also a pretty simple relationship between initial height and range — if a ball starts off higher above the ground, it will go farther.

What about launch angle? Is it immediately obvious what launch angle will give the farthest range? In this sports science project, you will specifically do an experiment to find out the best launch angle to give the longest possible range (while doing your best to keep the other variables constant). Do you think there is an "ideal" launch angle that will give the longest possible range?

## Terms and Concepts

• Projectile
• Projectile motion
• Gravity
• Air resistance
• Parabola
• Range
• Initial speed
• Launch angle
• Initial height

### Questions

• How do forces like gravity and air resistance affect a football as it moves through the air?
• What is a parabola? What is the difference between a parabola and a circular arc?
• What happens to the range of a projectile if you increase its initial speed, while you keep the initial height and launch angle constant?
• What happens to the range of a projectile if you increase its initial height, while you keep the initial speed and launch angle constant?
• How do you think launch angle will affect the range of a projectile? For example:
• How far will the ball go (horizontally) if you throw it straight forward (a launch angle of 0°)?
• How far will the ball go (horizontally) if you throw it straight up (a launch angle of 90°)?
• How far will the ball go (horizontally) if you throw it diagonally (at an angle of about 45°)?
• What angle do you think will give the longest range?

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## Materials and Equipment

• Football; available from a local sporting goods store or Amazon.com.
• Note: You can do this science project for any sport that involves throwing or kicking a ball. The only requirement is that the ball has to be big enough to easily see when using a video camera from far away. For example, a soccer ball would work very well, but a golf ball would not.
• Digital video camera
• If you want to use a cell phone to record video, make sure to use a phone with a reasonably high-quality camera. You will also need to be able to mount the phone on a tripod, which may require an adapter.
• Tripod; available from Amazon.com.
• At least 3 volunteers to throw the football
• Large, open area in which to throw the ball (like an empty football field)
• Computer with internet access, and permission to install programs
• Measuring tape
• Lab notebook

## Experimental Procedure

Reminder: This procedure is written assuming you will be throwing a football, but you can adapt the project to work with kicking or punting a football, or for another sport, like soccer or basketball.

1. Bring your football, camera, tripod, lab notebook, pen or pencil, and three volunteers to a large, open area where you can safely throw the football without hitting other people or buildings. Note: Don't forget to charge your camera beforehand, and make sure it has its memory card.
2. Set up your camera on the tripod so its view is perpendicular to the direction in which your volunteers will be throwing the football, as shown in Figure 3. This is important so the projectile's path will not be distorted when you track it using motion-tracking software later.

A camera is placed perpendicular to the trajectory of a thrown ball at about the half-way point between the throw and the landing area. Cameras placed at an angle to the trajectory of the ball won't be able to successfully film the thrown ball.

Figure 3. A top-down view of the experiment setup. Make sure the camera's view is perpendicular to the direction in which your volunteers will be throwing the ball.
1. Make sure your camera is far enough away that you can capture the entire parabolic motion of the ball in the camera frame, without moving or re-aiming the camera. You will need this to analyze your data in the motion-tracking software later.
1. Have a volunteer stand all the way on the left edge of the view frame from your camera. Make sure he/she is still visible in the frame and does not walk off-screen.
1. Throwing from left to right will make your data consistent with the convention that the x-axis (or horizontal axis) in an x-y plot is positive to the right and negative to the left.
2. Have the volunteer throw the ball as far as he/she can (to your right), while you are looking at the viewfinder or preview screen in your camera.
1. If the football goes off the top edge of the screen, or goes off the right side of the screen before it hits the ground, then your volunteers need to be farther away from the camera.
2. Move your tripod backwards (or ask your volunteers to stand farther away) and repeat this process until the ball never leaves the camera frame.
2. Explain to your volunteers that you will be asking each of them to throw the football as hard as they can at three different angles: a shallow angle, a medium angle, and a steep angle. These angles should correspond to roughly 15°, 45°, and 75°, as shown in Figure 4.
1. If you printed a copy of this procedure, show Figure 4 to your volunteers.
2. If anyone has a smartphone, you can view the project directions online and show Figure 4 to your volunteers.
3. Explain to your volunteers that it is okay if they cannot control the angle of each throw exactly. Even a professional quarterback could not do this! It will be easier to think about each type of throw qualitatively:
1. A "shallow" throw is almost straight out, but angled a little bit upward.
2. A "medium" throw is diagonal, out and upward.
3. A "steep" throw is almost straight up, but also a little bit forward.
4. Remind your volunteers that it is important that they throw the ball using the same method each time. For example, do not switch between throwing the ball overhand and underhand.
5. Explain to your volunteers that it is very important that they consistently throw the ball as hard as they can. Remember that initial speed can have an impact on a projectile's range. You only want to test launch angle as an independent variable in this experiment, so you want to keep initial speed as consistent as possible for each volunteer.
6. Remember that initial height also affects a projectile's range. You will look at the data individually for each volunteer, to account for any large differences in height (small differences in height will not matter very much) or large differences in initial speed between volunteers.

Figure 4. A diagram of 15° (shallow), 45° (medium) and 75° (steep) launch angles.
1. Record data for your first volunteer.
1. Tell your volunteer he/she will throw the ball 5 times at each angle, for a total of 15 throws.
2. Record a video for each throw. Be sure to start the camera before the volunteer throws the ball, and stop it after the ball hits the ground.
1. Always make sure your volunteer throws from left to right on the camera.
2. At the beginning of each video (before the volunteer throws the ball), make an announcement so you know which trial you are on. This will help you keep track of your videos later. For example, you could say "(Volunteer's name), shallow angle, first throw" for the first trial, and "(Volunteer's name), steep angle, fifth throw" for the last trial.
3. If the volunteer ever has a particularly bad throw (for example, they really mess up the intended angle, or accidentally do not throw the ball as hard as they can), delete the video and redo the trial.
2. Repeat step 5 for each remaining volunteer. You should have a total of 45 videos, 15 for each volunteer.
3. Before you leave, measure and record each volunteer's height, in meters, in your lab notebook, using a table like Table 1. You will need this information later when you analyze your videos. If necessary, you can use an online unit conversion tool to convert feet and inches to meters.
 Volunteer Name Height (meters) Height (feet and inches)

Table 1. A data table in which to record each volunteer's height. If you initially record the heights in feet and inches, make sure you convert them to meters later.

1. Create a data table like Table 2.
1. Optional: Using a spreadsheet program like Microsoft® Excel® will make it easier to graph your data later.
 Volunteer Name Launch Angle (Shallow, Medium, Steep) Throw # Actual Angle (degrees) Range (meters)

Table 2. A data table to keep track of your results. For three volunteers and 15 throws each, your table will need a total of 45 rows.
1. Your video camera probably assigned file names to your videos, such as "MVI_0001.mov" or "VID_001.mts" (the file extension will vary depending on the camera). You should rename your video files based on each trial, to help you keep better track of them later. For example, you could rename your files using the convention "volunteername_angle_trial#.mov", e.g. "Susie_shallow_1.mov".
2. Follow the instructions at http://www.cabrillo.edu/~dbrown/tracker to download and install the Tracker Video Analysis and Modeling Tool, from now on just referred to as "Tracker."
1. Tracker is a program that lets you play a video file back frame-by-frame. In each frame, you can click on the ball, and Tracker will save its horizontal and vertical position as a pair of (x,y) coordinates. This makes it easy to track the trajectory of your ball.
2. Note: This procedure will provide some general instructions for using the Tracker program, but is not a step-by-step tutorial for using Tracker. If you are having a difficult time using the program, you can ask an adult for help, and read the Getting Started instructions on the Tracker website.
3. In Tracker, select File → Open and open your first video file. You should see a screen like Figure 5.
1. Note: This science project was written in November 2013 using Tracker Version 4.82. Future versions of Tracker may not look exactly like what is shown in Figure 5. If at any point these instructions do not match what you see in your Tracker window, check the Tracker help instructions by selecting Help → Tracker Help from the top menu bar.

A video is loaded into the program Tracker Video Analysis and Modeling Tool. The video appears in a player on the left side of the program and playback controls are underneath the video near the bottom of the screen.

Figure 5. A video file opened in the Tracker program.
1. Create a calibration stick. Once your calibration is done, the distances indicated in Tracker will correspond to the real-life distances.
1. From the top menu bar, select Tracks → New → Calibration Tools → Calibration Stick.
2. This creates a new calibration stick in the middle of your screen. The default length is 100 units.
3. Drag the ends of the calibration stick so it measures the height of your volunteer in the video, as shown in Figure 6.
1. You can use your mouse's scroll wheel to zoom in and out on the video if necessary.
4. In the text box next to the calibration stick (or the Calibration Stick menu at the top of the screen), enter the volunteer's height in meters, as shown in Figure 6.
5. If you need more help using the calibration stick, select Help → Tracker Help from the top menu bar, then Calibration Stick from the left menu in the pop-up help window.

Figure 6. A calibration stick (blue line) is used to scale the video to real-world distance units. In this case, the volunteer is 1.6 m tall.
1. Set the origin of the coordinate system.
1. Click the "Show or hide the coordinate axes" button in the top toolbar, as shown in Figure 7.
2. This will display a set of coordinate axes on screen, like in Figure 8.
3. Click and drag the origin of the coordinate system toward your volunteer.
4. Use the playback control toolbar at the bottom of the screen to advance to the point where your volunteer throws the ball. Stop on the first frame immediately after the ball leaves the volunteer's hand. Drag the origin of the coordinate system onto the center of the ball, as shown in Figure 8.
5. To read more about setting coordinate systems in Tracker, select Help → Tracker Help → Coordinate System.
6. Note: Depending on the type of digital camera and the recording mode you used, you may need to apply a deinterlacing filter to your video. See Figure 9.
1. To apply a deinterlacing filter, select Video → Filters → New → Deinterlacing. Select either Odd or Even (depending on which one makes your video look better), then click "Close."

In the top navigation bar in the Tracker program there is a graph button to show or hide an overlaid coordinate plan over the video.

Figure 7. The "Show or hide the coordinate axes" button.

 Figure 8. Coordinate system axes displayed in magenta on the screen. By default, the axes are centered in the middle of your video (top image). You need to click and drag the origin of the axes onto the center of the football in the first frame where it leaves the volunteer's hand completely (bottom image).

Figure 9. If your video looks like the image on the left when you zoom in, you need to apply a deinterlacing filter. The image on the right shows the video after applying a deinterlacing filter.
1. Save your work! Clicking the "Save" button in the upper left will allow you to save your setup so far, including the calibration stick, coordinate axes, and deinterlacing filter (if any), as a "tracker" file with the extension ".trk". Be sure to give the file a name that makes sense (e.g. the same naming convention as your video files) when you save it.
2. Track the location of the ball.
1. From the top menu bar, select Tracks → New → Point Mass. This will create a new tracked object in the file, which you will use to follow the ball's position in each frame.
2. If you are not there already, use the playback controls to move the video to the first frame after the ball leaves the volunteer's hand.
3. Zoom in on the ball using the mouse scroll wheel. Hold down the "Shift" key and click on the center of the ball. This will mark the ball's location and automatically move the video to the next frame.
4. Keep holding down "Shift" and clicking on the center of the ball in each frame, until the ball hits the ground.
5. Remember to periodically save your work!
6. Click the "Set trail length" button in the top menu bar and select "All steps," shown in Figure 10.
7. Your Tracker window should now look something like Figure 11.

In the top navigation bar in the Tracker program there is an icon with small green dots that can be pressed to set a trail length for the trajectory of a thrown object.

Figure 10. The "Set trail length" button.

Figure 11. All of the tracked points for a complete throw.
1. Use the data table in Tracker to record the range.
1. The lower right-hand corner of the Tracker window has a table with columns labeled "t", "x", and "y". They stand for time (in seconds), x position (in meters), and y position (in meters).
1. Note: There are small arrow buttons that can minimize the "Table" area. If you do not see the table at all, you may have accidentally minimized it. Ask an adult for help or read the Tracker help files to find out how to re-open the table.
2. Scroll down to the end of the table and look at the very last "x" value. This is the horizontal distance your ball traveled before it hit the ground. Record this value under "Range" in the data table you made in step 1 of this section.
2. Use the Protractor tool to measure the launch angle.
1. From the top menu bar, select Tracks → New → Measuring Tool → Protractor. This will bring up a protractor on the screen.
2. Click and drag the protractor to measure the launch angle of the ball, by measuring the angle between the first two tracked points and the horizontal coordinate system axis, as shown in Figure 12.
3. Enter the launch angle in your data table.

Figure 12. This zoomed-in view of the protractor (green) shows a launch angle of 57.8°, measured between the coordinate axes (purple) and the first two data points (red). The numbers 96 and 97 correspond to the 85th and 86th frames of the video, the first two frames after the ball leaves the thrower's hand.
1. Export the tracking data. Tracker allows you to make graphs and analyze only one video file at a time. For this science project, you will need to make graphs to compare multiple trajectories at once. To do so, you will need to export the data to a format you can use in another spreadsheet program, like Microsoft Excel.
1. From the top menu bar, select File → Export → Data file...
2. In the window that pops up, make sure you have the following options selected:
1. Data Table: Mass A
2. Cells: All Cells
3. Number Format: As Formatted
4. Delimiter: Comma
3. Then, click "Save As", and save the data file as a comma-separated variable, or csv file.
1. Important: Tracker does not automatically add the file type extension. You will need to type ".csv" after your file name.
2. Use the same file-naming convention you have used for your videos and Tracker files, e.g. "volunteername_angle_trial.csv".
2. Repeat steps 4–11 for each of your remaining videos. Here is a summary of the steps:
1. Open a new video file.
2. Create a calibration stick.
3. Set the origin of the coordinate system.
4. Save your work frequently! Remember to stick with your file-naming convention.
5. Track the location of the ball.
6. Record the ball's horizontal range.
7. Use the Protractor tool to record the launch angle.
9. Export the tracking data as a .csv file.
1. Use your data from Table 1 to create a scatter plot with launch angle on the x-axis and range on the y-axis.
1. Color-code the data for each volunteer so you can tell them apart. This is because you should not directly compare data between different volunteers; different throwers might have different initial heights or initial speeds for the ball, meaning the comparison would not be valid.
2. Do you notice a trend in the data? Does it look like there is a launch angle (or angles) that tend to give the longest range?
3. How does this trend (if any) line up with your prediction about the relationship between launch angle and range?
2. Use your saved .csv files to make plots of each ball's trajectory.
1. Import the .csv files into a spreadsheet program like Microsoft Excel. This may be easiest if you import each file into a new tab. Ask an adult if you need help.
2. For each volunteer, make a line graph including each throw's trajectory, with horizontal position (in meters) on the x-axis and vertical position (in meters) on the y-axis.
3. If you make one graph for each volunteer, with all of their throws on one graph, you should have three graphs, each with 15 lines. Making one graph for each volunteer will help you account for possible differences in initial height and speed of the ball between different volunteers.
4. Color-code the lines by launch angle. For example, you could use blue for "low" angles, green for "medium" angles, and red for "steep" angles.
5. Do you see an obvious difference in the trajectories of the balls for the different launch angles? Does one group of launch angles tend to make the ball go farther before it hits the ground?
.

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## Variations

• Repeat the experiment using a different method of launching the same ball. For example, compare throwing, kicking, and punting a football. Is the best angle to achieve the longest range the same in all three cases?
• Do the experiment to compare two different sports; for example, kicking a soccer ball versus kicking a football. Is the best angle to achieve the longest range always the same for each sport?
• Think of a way to have your volunteers keep their launch angles as constant as possible, and vary the ball's initial speed instead. You can use Tracker to measure the ball's initial speed (read the Tracker help files to find out how).
• In the Introduction, you learned that the range of a projectile depends on its launch angle, initial speed, and initial height. If you assume the initial height is the same as the final height, the range can be expressed using Equation 1 (the equation is more complicated if the initial and final height are different):
• Equation 1:
• R is the projectile's range in meters (m)
• v0 is the projectile's initial speed in meters per second (m/s)
• g is acceleration due to gravity, 9.81 meters per second squared (m/s²)
• Can you use this equation to predict the football's range, based on the launch angle and initial speed you measure in your video? How does the predicted range compare to the actual measured range, and what could account for any difference?
• Can you use the equations of projectile motion to predict what launch angle should give the longest horizontal range?
• Remember to account for any elevation difference between where the ball starts and where it hits the ground. For example, the answer is different if you are kicking a football off the ground (initial height of 0 m) versus throwing it (initial height of about 2 m).
• Can you fit a quadratic equation to the (x,y) coordinates of your trajectories? How close are they to a perfect parabola, and what role do you think air resistance plays in the difference (if there is one)?

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