Some problems of the projectile motion with a square-law resistance

Abstract

The influence of the force of the quadratic resistance of the medium on the change in some interesting characteristics of the motion of the projectile, which take place when the projectile moves in vacuum, is investigated. Loci are constructed numerically (and partly analytically) that ensures maximization of the arc length of the projectile trajectory and a non-decreasing of the length of the radius-vector. As examples, the motion of a baseball, a tennis ball and a badminton shuttlecock is studied.

Projectile motion in a medium with quadratic drag at wind influence

“…Here we state the formulation of the problem and of the equations of the motion [4]. Let us consider the motion of a projectile with mass m launched at an angle θ 0 with an initial speed V 0 under the influence of the force of gravity and resistance force 2…”

“…The main problem in calculating integrals (8) is that the complex form of the transcendental function () f  in the velocity hodograph equation does not allow to find a solution in elementary functions. In this paper, we propose a convenient solution of the problem taking into account the wind, similar to the solution in [4]. According to the approach used in [2], we divide the entire range of the trajectory angle 0 /2…”

“…In [2], analytical approximations were obtained to describe the motion of a projectile with quadratic drag, were then they used in [3]. In article [4], these approximations are used to study motion taking into account a constant horizontal windIn this work, within the framework of the same approach, the motion of a projectile is studied in the presence of both horizontal and vertical wind components. The purpose of this study is to construct fairly simple analytical formulas that describe with acceptable accuracy the motion of a projectile in a medium with quadratic resistance under the action of wind.…”

“…Without taking into account the wind, this was done in [2], based on the idea of the work [6]. In article [4], the velocity hodograph equation with the adopted wind model taking into account and analytical approximations [2] are combined. In this study the conditions of applicability of the quadratic resistance law are deemed to be fulfilled, i.e.…”

Relativistic mean proportion

“…Teaching is a much more important branch of physics than one might think. Indeed, it may also happen that concepts of classical physics, well known to specialists, require further study from a didactic point of view due to the young age of the students [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. Generally during the last year of high school, students learn that SR is founded on the principle of relativity and on the fact that the speed of light is a fundamental constant of nature and it does not follow the Galilean law of addition.…”