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This lesson utilizes digital video in giving students a clearer understanding of the motion of projectiles. The lesson encompasses two parts. The first part pertains to projectiles that are launched horizontally and the second part deals with projectiles launched at an angle.
The students produce short video clips and then project the video onto a white board in a series of stop frame pictures. The flight path is then recorded on the board and measurements of distance and time may be used to analyze the motion.
The usual objective of projectile motion problems is to determine the range and height of a projectile that has been fired at a known velocity and angle. In this activity we use digital video and still pictures to measure and calculate the horizontal and vertical components of the initial velocity and the launch angle. With this information, we then calculate the range and the height and compare the results to the actual measurements.
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Students will be able to:
- Utilize video and still images in calculating velocity in two dimensions.
- Utilize velocity and acceleration data to determine range of projectiles.
- Understand that vertical and horizontal velocities are independent in projectile motion.
- Show that projectile motion follows a parabolic path.
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- Large cart with wheels (an office chair on wheels may also work)
- Tape measure
- Projectile (baseball or other heavy object)
- Digital video camera
- LCD projector
- Empty hallway or gymnasium
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| | | | | Horizontal Projectile Motion | | |  | |
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Set up the camera on a tripod so that the camera is level and has a wide view of the drop zone. It is also preferable to have a simple background. Avoid setting up in front of bulletin boards and other busy backgrounds. Layout a target on the floor in the path of the drop zone.
- One student (bombardier) will need to sit on the cart.
- One or two students will push the cart (pilots). Their objective is to push at a constant velocity and release the cart just prior to the target.
- Two or three other students may be designated to signal when the bombardier should drop the projectile. This is most easily done by trial and error. The bombardier should simply drop the projectile, trying to be consistent with the height at which it is dropped.
- After practicing, two or three recordings are made until the target is hit. During this trial the height from which the projectile is dropped should also be measured. This may be done (when the cart is still) by measuring the height of the bombardier’s hand when it is in the position to drop.
- Once a good video is made, the camera can be set up to play through an LCD projector onto a whiteboard in the class room. The video may be watched a few times at normal speed and then it should be shown frame by frame. At the same time, a student should use a dry erase marker to record where the projectile is in each frame. The relative horizontal and vertical distances between successive marks should show that the horizontal distances are fairly constant and the vertical distances are increasing. Therefore the projectile is in fact accelerating in the vertical direction. The diagram at the top of this page is a good illustration of what the board will show.
- From the height measured while making the video and the time elapsed from the video playback (recorded by the camera or calculated knowing the frame rate of the camera), the acceleration of the projectile may be calculated. It should be very close to the accepted value of the acceleration due to gravity (9.80 m/s2).
- Optional: The horizontal velocity of the projectile may be measured with a motion detector or by measuring time and distance. This velocity may be used to calculate the range of the air drop by the following equations and then compared to an actual measurement of the drop. The calculation should open the door for a discussion regarding the affects of air resistance.
- Optional: The above procedure is also an excellent way to lead into a derivation of the equations used to calculate range of projectiles given the initial velocity and the height.
- Optional: Videos may also be used to show that projectiles launched at an angle will adhere to the same formulas. A video of a student tossing a ball will yield data that will enable you to make calculations like the ones listed above.
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| | | | | Projectile Motion with Angled Launch | | | | |
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In this activity a student will throw a baseball or other projectile in the air at an angle. The students videotape the flight of the projectile and then record the height and range. The video is then projected onto a whiteboard and more measurements of angles and distance may be made. The students may then calculate the initial velocity and the range and compare the results of their calculations to the measured results.
- Set up the video camera on a tripod with the target area in view. The location should be in a large hallway or gymnasium so that a sufficient area may be seen by the camera. Set up a tape measure to measure the horizontal range and a meter stick to measure the height.
- Start the video camera and have a student toss a ball at a 45 degree angle or more. It is important that the whole flight of the projectile is within the frame of the video. As the ball is tossed other students should make note of the range and the height.
- When a good trial is obtained, the video may be projected onto a whiteboard. The video should be played at regular speed and then a single frame at a time. As the video is played a single frame at a time, a student should mark the position of the ball in each frame on the whiteboard.
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Click the attachment icon to download a Word document that lists the calculations below. The file also includes the formulas used to determine the answers to questions 2, 3, and 4.
- Measure and record the angle at which the ball is launched.
- Calculate the initial horizontal velocity. Measure the horizontal distance the ball travels in the first 5 frames and divide by the time per 5 frames (1 frame = 1/30 sec).
- Use the initial horizontal velocity to determine the initial velocity.
- Use the initial velocity and the angle of launch to calculate the range and height.
- Compare results to the range and height measured.
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