A Unifying Rule for Maximizing the Range or Minimizing the Launch and Impact Speed of a Projectile Along a Tilted Plane (Journal Article)

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Abstract: The motion of a projectile moving under the influence of gravity in the absence of air resistance has been analyzed many times in this journal. For example, there have been articles devoted to the details of the path of a projectile1–4 and different launching situations.5–7 Other papers have looked at determining the maximum height of a projectile,8 finding the range of a projectile under very general circumstances,9 and hitting a moving target.10 Finally, some articles detailed engaging ways to incorporate projectile motion in the classroom or laboratory.11–13 In this paper, we will rederive a rule that dictates the launch angle maximizing the range, but generalize it to include minimizing the launch and impact speed of a projectile along a tilted plane.