Critical Launch Angle for Projectile Motion | ||
| ERU Research Journal | ||
| Volume 3, Issue 3, July 2024, Pages 1471-1479 PDF (298.07 K) | ||
| Document Type: Original Article | ||
| DOI: 10.21608/erurj.2024.251675.1095 | ||
| Authors | ||
| Amira R. Abdel-Malek* 1; Ola Siam2 | ||
| 1Department of Mathematical and Natural Sciences, Faculty of Engineering, Egyptian Russian University, Badr City, Cairo, Egypt. | ||
| 2Department of Mathematical and Natural Sciences, Faculty of Engineering, Egyptian Russian University, Badr City, Cairo, Egypt. | ||
| Abstract | ||
| In this research article, we have successfully demonstrated an interesting characteristic of parabolic motion when the launch angle is at a critical value. Specifically, we have discovered an unexpected property associated with the distance between the launched object and the launcher. This property exhibits both a maximum and a minimum distance. We will illustrate that this phenomenon occurs only when the launch angle exceeds a certain threshold, specifically when . It is essential to highlight that our investigation of the launch scenario assumes a ground-level launch and does not account for the effects of air resistance. To emphasize the angular variable, we used dimensionless coordinates in our analysis. Critical launch angle is a key parameter determining the optimal angle for maximizing range and accuracy in projectile trajectories. This study offers a refined method to optimize trajectories for maximum efficiency and precision across various applications, enhancing performance and control. It can be used in various fields, such as sports and civil engineering. | ||
| Keywords | ||
| parabolic motion; motion in two dimensions; projectile; launcher | ||
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