A flight simulator is used to train pilots on how to recognize spatial disorientation. It has four degrees of freedom, and can rotate around a planetary axis as well as in yaw, pitch, and roll. The pilot is seated so that her head B is located at r = 2i + 1j ft with respect to the center of the cab A. Knowing that the cab is rotating about the planetary axis with a constant angular velocity of 20 rpm counterclockwise as seen from above, and pitches with a constant angular velocity of +3 k rad/s, determine 

(a) The velocity of the pilot's head, 

(b) The angular acceleration of the cab, 

(c) The acceleration of the pilot's head.

Planetary axis Yaw OB Roll Pitch 8 ft