Based on the dynamic differential equations of a free-falling particle and an upward casting particle in the non-inertial system，the accurate solutions of the particle’s coordinates are obtained.Then the eastward and westward drift for the two problems are obtained.Expressions of the kinetic energy and potential energy are also obtained. It is demonstrated that the mechanical energy conserves to a constant during the movement. In the numerical examples，we discuss the values of drift with different initial height or initial velocity.