Projectile Motion: Finding the Optimal Launch Angle

Projectile Motion: Finding the Optimal Launch AngleNina HenelsmithWhitman CollegeMay 12, 20161 AbstractIf we want to throw a Projectile as far as possible, at what Angle should it be launched?This paper focuses on how the answer to this question changes depending on the look at launching projectiles onto di erently shaped hills, as well as how varying initialvelocity and height a ect the Launch Angle . Finally, we add air resistance to the projectileproblem and compare two di erent models: air resistance proportional to the Projectile svelocity and air resistance proportional to velocity you to Professor Russ Gordon for his helpful support and guidance for this you also to Karen Vezie, for her valuable edits and comments, and to ProfessorBarry Balof, for teaching the Senior Project math class and providing useful project Introduction42 The Projectile problem43 equations of motion: no air resistance54 The Optimal Launch The distance function.

We now have a set of parametric equations for the motion of the projectile as a function of t, but to maximize the projectile’s horizontal distance, we want to find a path function, p, that defines the projectile’s height as a function of horizontal distance, x. Solving for t in (1) and substituting into (2) yields t = x vcos , and therefore

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  Solving, Equations, Distance

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