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A classic problem of the motion of a projectile thrown at an angle to thehorizon is studied. Air resistance force is taken into account with the use ofthe quadratic resistance law. The action of the wind is also taken intoaccount, which is considered constant and horizontal. The projectile velocityhodograph equation is used to account for the effect of wind. Comparativelysimple analytical approximations are proposed for the main variables of motion(cartesian projectile coordinates and time). All obtained formulas contain onlyelementary functions. The proposed formulas are universal, that is, they can beused for any initial conditions of throwing. In addition, they have acceptableaccuracy over a wide range of the change of parameters. The motion of a golfball, a tennis ball and shuttlecock of badminton are presented as examples. Thecalculation results show good agreement between the proposed analyticalsolutions and numerical solutions. The proposed analytical formulas can beuseful for all researchers of this classical problem.

Projectile motion in a medium with quadratic drag at constant horizontal wind