Effect of coriolis force on a projectile shot along the earth's surface

Let P represent a location on the earth's surface at latitude λ. Take into account a rectangular Cartesian coordinate system with P as the swiftly fixed origin. The system's z axis is measured radially outwards from the earth's center, or vertically upward at P.

The X-Y plane is the horizontal plane that contains the point P, with the X axis heading eastward and the Y axis pointing in the same direction as the X axis, which is taken to be positive. The angular velocity is parallel to the polar axis around which the earth spins and is located in the Y-Z plane. Therefore, the vector w has no component in the east-west direction.

This note is taken from Classical Mechanics, MSC physics, Nepal.