An analytic approach to projectile motion in a linear resisting medium

Stewart, Seán M.

doi:10.1080/00207390600594911

Cited by 24 publications

(22 citation statements)

References 23 publications

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“…( 20) is known from the literature, although its derivation is customarily carried out by first solving the time-domain dynamical equation (10) and only after removing the variable t among the functions x = x(t) and y = y(t). 4 It is also worth showing to the student how, for small values of drag force, the shape of the trajectory tends to become identical to the ideal free-friction case of Eq. ( 9).…”

Section: Trajectory Of a Body In Vacuummentioning

confidence: 97%

Trajectory of a body in a resistant medium: an elementary derivation

Borghi¹

2013

Eur. J. Phys.

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A didactical exposition of the classical problem of the trajectory determination of a body, subject to the gravity in a resistant medium, is proposed. Our revisitation is aimed at showing a derivation of the problem solution which should be as simple as possible from a technical point of view, in order to be grasped even by first-year undergraduates. A central role in our analysis is played by the so-called "chain rule" for derivatives, which is systematically used to remove the temporal variable from Newton's law in order to derive the differential equation of the Cartesian representation of the trajectory, with a considerable reduction of the overall mathematical complexity. In particular, for a resistant medium exerting a force quadratic with respect to the velocity our approach leads to the differential equation of the trajectory, which allows its Taylor series expansion to be derived in an easy way. A numerical comparison of the polynomial approximants obtained by truncating such series with the solution recently proposed through a homotopy analysis is also presented.

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Section: Trajectory Of a Body In Vacuummentioning

confidence: 97%

Trajectory of a body in a resistant medium: an elementary derivation

Borghi¹

2013

Eur. J. Phys.

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“…Also, Zhao [19] used the same Lambert W function and concluded that the higher the projection point, the wider the range and slighter optimal angle it become. Moreover, [10] [19] [20] have looked into how the Lambert W function used to figure out how a projectile moves when it has linear drag, while in [21] [22] examine the Excel spreadsheets that castoff the simulation of projectile motion with air resistance before [8] [23] [24] [25] [26] talk about the history of projectile motion in the real world. [23] [27] [28] wrote about the results of experiments where sports balls were used as projectiles.…”

Section: Introductionmentioning

confidence: 99%

Computational Solution to the Problems of Projectile Motion under Significant Linear Drag Effect

Said¹,

Mshewa²,

Mwakipunda³

et al. 2023

OJAppS

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This paper investigates the computational solution to the problem of projectile motion under a significant linear drag effect. The drag force acting on the particle within the medium of propagation is proportional to the cross-section area of the projectile, the velocity of the particle, and the medium's density. From zero air resistance force (vacuum) the problems are well known with solutions, but with air resistance (drag force) the problems have no exact analytical solutions which lead to most of the significant scientific research works using numerical methods. Therefore, this study aims to present the analysis of the computational modelling of drag force exerted by the surrounding medium on the linear motion. However, the horizontal and vertical components of differential equations of motion were derived and characterized from the solutions governed by Newton's 2 nd law of motion. The baseball features were presented as the projectile (object) in this work. In addition, the numerical computational results were received from FreeMat. The results were discussed and compared with those from the vacuum. Moreover, the displacements, velocities, range, and trajectories of the projectile were all discussed and a conclusion was made.

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“…Since neglecting the resistant force to projectile motion is impractical, is desirable to develop analytic solutions from a simplified model so as to elucidate some of the essential features and structure of this problem. The linear model, in which the resistance is taken to be proportional to the instantaneous velocity of the projectile, is generally accepted as the first approximation to such resistive behavior [8,9] and it is the model we use here. Simulation of the projectile's motion with and without drag forces is extended.…”

Section: Introductionmentioning

confidence: 99%

Horizontal projectile motion: comparing free fall and drag resistance

2020

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The motion of a particle that is projected into a resistant medium and subjected to a uniform gravitational field is considered. The drag force that acts upon the particle within the medium is proportional to the particle’s speed, the density of the medium, and the cross-section area of the projectile. We review the problem of a horizontal motion with a drag force that is linear in speed. The problem is formulated in terms of particle speed, mass, height, time, and expelled gas velocity. The equations of motion are solved analytically, and a case study is discussed. As a result, we obtain the deviation of the projectile as a function of time because of the expelled gases with or without drag force.

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An analytic approach to projectile motion in a linear resisting medium

Cited by 24 publications

References 23 publications

Trajectory of a body in a resistant medium: an elementary derivation

Trajectory of a body in a resistant medium: an elementary derivation

Computational Solution to the Problems of Projectile Motion under Significant Linear Drag Effect

Horizontal projectile motion: comparing free fall and drag resistance

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