At a certain instant, gyrosensors on an airplane report that it is heading 40 degrees west of north, climbing at an angle of 20 degrees, and that its wings are banked at an angle 10 degrees clockwise as looking forward (along the axis of the plane). At this instant, the aircraft's accelerometers indicated that the center of mass has acceleration components relative to the aircraft of 2g downward and 0.5g forward. What are the acceleration components in terms of north-south, east-west, and vertical? Set up the fixed coordinate system such that X is to the north, Y is to the west, and Z is vertical.