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

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.