A Simple General Solution for Maximal Horizontal Range of Projectile Motion.pdf

arXiv:physics/0505069v1 [-ph] 10 May 2005 A Simple General Solution for Maximal Horizontal Range of Projectile Motion Boris Buˇsi′c Ksaver 173, Zagreb, Croatia ?(Dated: February 2, 2008) Abstract A convenient change of variables in the problem of maximizing the horizontal range of the projectile motion, with an arbitrary initial vertical position of the projectile, provides a simple, straightforward solution. ?Electronic address: ******@hi..hr 1 I. INTRODUCTION A clear, concise formulation of the general solution for maximal horizontal range of the projectile motion is considered non-trivial. Consequently much e?ort has been spent to formulate a solution that would be understandable to as wideaudience as possible. The problem may be stated as follows: Find the maximal horizontal range,R, of a projectile launched with an initial speedv 0 from the point with the vertical coordinatey 0. (Figure 1) Generally the known solutions are divided into those that doand those that do not make use of calculus. Somewhat misleadingly the former monly quali?ed as simple. The categorization according to whether a solution starts from the vector or scalar general solution of projectile motion seems more appropriate. In the former one starts from ~r=~r 0+~v 0t+ 12 ~gt 2 ~v=~v 0+~gt (1) and employs “ingenious application of vector algebra, involving both dot and cross products”(citat