An object given an initial velocity near the Earth's surface undergoes two different motions at the same time. In the horizontal direction, the amount of air resistance may be quite small so the motion is essentially constant velocity. In the vertical direction, gravity acts in a constant and downward direction resulting in a constant acceleration. This study explores projectile motion and can be extended based on the abilities of the students and the goals of the individual course.Purpose:
Equipment:Study the motion of an object in projectile motion.
This description assumes the use of a Vernier Projectile Launcher (VPL). A computing device running Vernier Graphical Analysis 4 or Logger Pro or LabQuest app completes the equipment, although meter sticks or measuring tapes are useful. Some other equipment alternatives are described below.1Procedure:
Calibration -
Follow the directions to set up the VPL so it launches the ball horizontally. Set the apparatus on a long table and launch the ball several times, noting the horizontal distance to where the ball lands. For each launch, record the launch speed as noted in the software. Use the launch height of the apparatus and the horizontal distance to calculate the launch speed. Compare the electronic measurement with the calculation. How well to they agree?Testing -
Note that any arrangement that launches horizontally could be used. Although a launch speed might not be determined electronically, the speed can be determined by the projectile motion.
Once the launch speed is established, turn the launcher so the ball goes off of the table and lands on the floor. Students calculate how far the ball will travel before landing. Then launch 5-6 times and take the average distance to compare with their calculations. A fun activity is to locate a cup, say from a frozen juice can, where they think it will land and see if they can hit it.Range vs. Angle -
Use the VPL set to a range of angles in 5-degree increments, recording the angle and range of the projectile. Graph Range vs. Angle. Experimentally, what angle gives the greatest range?Advanced Testing 1 -
Calculations of projectile motion can show the maximum range to be 45 degrees. Does the maximum range achieved during the experiment agree with this theory? Why might the results be different? Develop a method that will result in the maximum range being at a launch angle of 45 degrees. And determining angle with the maximum range is an excellent activity for AP students.
With the VPL, the launch speed is measured each time. Set a launch angle of perhaps 20 degrees. Launch from the table to the floor as before, but calculate the new landing distance. (Each group might be given a different launch angle.) How well does the range match up with the calculations?Advanced Testing 2 -
The launch speed of the VPL can be changed. Set a standard launch angle, or give each group a different angle. Give the class a horizontal distance for their projectile. They will need to adjust the launch speed to a value that they calculate. Award points based on how close they land compared to their required distance.
Some Thoughts
1 - A variety of ramps could be generated that will allow a marble or steel ball to roll down then exit in a horizontal direction. Typical 12" plastic rulers could be used, U-channel such as used with windows could be carefully bent, or even plastic tubing or foam pipe insulation could be employed. In a pinch, even a straight ramp with perhaps a groove to control the direction of the ball could end with the ball going horizontally across the table before becoming a projectile. While not able to electronically measure the launch speed in the same way as the VPL, photogates could be used to determine the launch speed of the ball.
I found a toy car of approximately the MatchBox size made in Germany that has a great wind-up motor. When rolled backwards the motor stores up energy in a spring until it maximizes out. It then rachets. Upon release, the car has a dependable speed. I launched the car from a position on top of a box on my desk to do the calibration. Then turned 90 degrees, it launched to the floor. Students placed their "target" on the floor and the AP students placed a ring stand ring about 60% of the way to the target that the car had to pass through.
While still on the topic of ramps, consider having the students calibrate their ramp for launch speed as a function of where they place the ball along the ramp. Then they might be challenged to hit a target a fixed distance away from their launcher and need to determine where to place and release the ball. The author utilized this technique with his AP classes as this was way before VPL. The ramps were in fact placed on top of a file cabinet giving an even greater height.
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Some of the discussion that arises in looking at the Range vs. Angle discrepancy is to discuss the difference between a projectile like a long jump athlete and the motion of the shot during a shot put. One launches from the ground and lands on the ground, while the other launches from perhaps 2 meters above the ground and lands on the ground. What angle should a shot putter attempt to use during his/her event? Does this depend at all on how tall the athlete is?
While on the subject of sports, this is a perfect place to bring in video of different events ranging from typical track and field, ball games, X-games, ski and snowboard events, etc. Or students could be tasked with developing their own videos. Or even consider non-sports activities like fountains and the path of the water spouts.
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Discussions of Projectile Motion would be incomplete if we didn't discuss using video analysis with projectiles. Logger Pro for Mac and PC has video analysis built in and Video Physics for iOS allows examination of projectiles. Both have a basketball shot as a sample, and the Basketball Shot activity on this site is quite useful. Consider using video analysis and employ a variety of objects like baseballs, soccer balls, Nerf balls, balloons, badminton birdies, etc.
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As before, if you have an idea that you would like to contribute to this study, send me a description and I will attempt to include it.
C. Bakken
11/13/19