Coriolis deflection of vertical launch and drop ($x_{\mathrm{launch}}=-4\Omega u^3\cos \lambda /(3g^2),x_{\mathrm{drop}}=-x_{\mathrm{launch}}/4$)

At first order in Earth's rotation, vertical velocity gives east acceleration $-2\Omega \cos \lambda \dot{z}$. A launch returning to its initial height lands westward, while a drop from the launch's maximum height lands eastward with one quarter the displacement magnitude. These results assume constant effective gravity, no air drag and no horizontal velocity in the Coriolis term. The northern component vanishes at this order.