A classic problem of the motion of a projectile thrown at an angle to the horizon is studied. Air resistance force is taken into account with the use of the quadratic resistance law. An analytic approach is mainly applied for the investigation. Equations of the projectile motion are solved analytically for an arbitrarily large period of time. The constructed analytical solutions are universal, that is, they can be used for any initial conditions of throwing. As a limit case of motion, the vertical asymptote formula is obtained.  The value of the vertical asymptote is calculated directly from the initial conditions of motion. There is no need to study the problem numerically. The found analytical solutions are highly accurate over a wide range of parameters. The motion of a baseball, a tennis ball, and a shuttlecock of badminton are presented as examples.

A local analytical solution for the problem of the motion of particle under quadratic drag force was constructed, and analytical formulae for main parameters of particle trajectory were obtained earlier by the present author. In this paper, we consider an application of these formulae. The determination of the motion kinematical parameters and drag coefficient from the measurement results is presented. In contradistinction to those results in open literature, simple analytical formulations for principal functional dependencies of the problem are constructed.

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The classic problem of the motion of a point mass thrown at an angle to the horizon is reviewed. The air drag force is taken into account with the drag factor assumed to be constant. An analytical approach is used for the investigation. Simple analytical formulae are used to solve two problems of optimization aimed at maximizing the flight range of a point mass and minimizing the initial speed of the point mass for getting to the given point on the plane. The motion of a baseball is presented as an example.

Here is studied a classic problem of the motion of a projectile thrown at an angle to the horizon. The number of publications on this problem is very large. The air drag force is taken into account as the quadratic resistance law. An analytic approach is used for the investigation. Equations of the projectile motion are solved analytically. All the basic functional dependencies of the problem are described by elementary functions. There is no need to study the problem numerically. The found analytical solutions are highly accurate over a wide range of parameters. The motion of a baseball and a badminton shuttlecock is presented as examples.