Calculating a Projectile's Trajectory

Overview

Objectives/Goals Our experiment was conducted for the purpose of determining which angle of a projectile launcher will achieve the greatest distance. We derived a mathematical formula to calculate the optimum angle and built a model projectile launcher to test the results. Methods/Materials To perform our experiment, we built a launcher that projected a ball bearing up to 2.5 meters. We tested our experiment by launching the ball bearing at seven different predetermined angles, with velocity as a constant. We conducted ten launches at each angle, measured the distance of each launch, created a chart showing each result, and calculated an average distance for each of the predetermined angles. Using this data, we derived a quadratic graph and equation that best matched the data. Results Using the graph's equation, we were able to determine which angle resulted in projecting the ball bearing the greatest distance. At an angle of approximately 34.73°, the projectile traveled its peak distance of approximately 210.13 cm. In addition, we were able to use the derived equation to predict the distance of future launches using different angles. Conclusions/Discussion Using calculations from a formula found in our initial research, we expected that a launch angle of 45° would result in the optimum distance of the launched projectile. Using our projectile launcher, we completed a set of test data and derived a formula that we compared against the formula from our research. Our outcome proved that the optimum angle was approximately 35°, significantly less than the predicted 45°. We concluded that this discrepancy was due to the fact that the established formula presumed conditions that did not include dynamics such as air resistance, friction, launcher inconsistency, and human error. The test conditions for our experiment included all of these factors. However, using the test data, we were able to derive our own mathematical formula that accurately predicted launch outcomes in our test environment.

Awards (1)

• Honorable Mention

Competition history

• CSEF 2007 Physics & Astronomy · Entry J1612

Resources

• CSEF project summary ↗

Related projects

Closest projects by meaning, across every fair and year in the corpus.

Browse more like this

• All Physics and Astronomy projects
• CSEF Physics and Astronomy projects
• Every CSEF 2007 project