In an inertial frame a free object moves in a straight line. The ground rotates under it with angular velocity Ω. In the rotating frame the equation of motion gains two fictitious terms: a = -2 Ω × v - Ω × (Ω × r). The first is the Coriolis acceleration, perpendicular to the velocity, magnitude 2Ωu sinφ on Earth. The second is the centrifugal term, pointing outward.
This map looks down on the pole. The white line is the inertial straight path; the yellow curve is the same motion drawn in ground coordinates, q(t) = R(-ωt) p(t). For short times the sideways drift is ωu t² (half of 2ωu times t²). The sense of the deflection is to the right in the northern and to the left in the southern hemisphere.
Simplifications: a flat disk stands for the polar cap (the launch ring radius is cosφ), the launch speed is in Earth radii per second, and the spin rate is far faster than the real 15 degrees/hour so the effect is visible. Real Earth: Ω = 7.292e-5 rad/s, so f = 1.03e-4 1/s at 45°. The numeric check integrates the rotating-frame equation with RK4 and compares it with the exact analytic path.