Analytical Solution of the Projectile Motion Under a Linear Drag Force.

Motion of a projectile in the absence of any resistive medium is quite ideal and has an exact analytical solution in classical mechanics. Ordinarily, projectiles move in a resistive medium which modify the acceleration of the body both in the horizontal and vertical directions. So far, the time of flight and the range arising from the solution of the classical problem due to the presence of a linear velocity‐dependent resistive force are not exact and can only be determined numerically. In this work, we attempt to solve the problem analytically. We resolve the underlying difficulty in the analytical problem by deriving an analytical function which guides the dynamics of the projectile and by calculating iteratively the falling time as a function of the maximum height reached. We show that the effect of the viscous drag force in the time of flight of the projectile may lead to time asymmetry in the upward and downward motion, reduced maximum height reached, time of flight, and range for any initial launching speed. The downward motion is established to take more time than the upward motion. We obtain excellent agreement between the calculated values and the computed trajectories. [ABSTRACT FROM AUTHOR]