Study of the projectile motion in the air using simple analytical formulas

Abstract

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. The projectile motion is described analytically with fairly simple formulas. They make it possible to calculate basic motion characteristics and trajectory as easily as in the case of a parabolic motion. There is no need to study the problem numerically. The proposed formulas are universal, that is, they can be used for any initial conditions of throwing. In addition, they have acceptable accuracy over a wide range change of parameters. The motion of a baseball, a tennis ball and shuttlecock of badminton are presented as examples.