  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 action of the wind is also taken into
account, which is considered constant and horizontal. The projectile velocity
hodograph equation is used to account for the effect of wind. Comparatively
simple analytical approximations are proposed for the main variables of motion
(cartesian projectile coordinates and time). All obtained formulas contain only
elementary functions. 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 of the change of parameters. The motion of a golf
ball, a tennis ball and shuttlecock of badminton are presented as examples. The
calculation results show good agreement between the proposed analytical
solutions and numerical solutions. The proposed analytical formulas can be
useful for all researchers of this classical problem.
