For a projectile going through thin air over some spot on the Earth, there is essentially no Coriolis force. The projectile passes over a particular spot on the Earth at t=0. A coordinate system, whose origin is at that particular spot, is locked to the Earth surface with its x-y plane tangent to the surface. This coordinate system rotates about its z-axis through an angle

t omega sin(latitude)

in a small time interval t. Omega is the angular rotation rate of the Earth about its polar axis. The projectile is moving at velocity v, so its lateral displacement from the point where it would have been in a non-rotating coordinate system is

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