  We consider the problem of the motion of a projectile thrown vertically
upward from a surface. In addition to gravity, the drag force of the medium is
taken into account, which is considered a quadratic function of the relative
velocity of the projectile. It is also assumed that the projectile is acted
upon by a wind that has a constant vertical velocity in magnitude and
direction. Analytical solutions of differential equations of motion, including
the influence of wind, are written down. As an example of the application of
the obtained formulas, the movement of a badminton shuttlecock is considered.
Various features of movement are considered, such as the shuttlecock hovering
in the air and continuous upward movement. The educational and methodological
significance of the obtained results for students of various levels of training
is noted.
