A frictionless bug sitting a top a bald man's spherical head is given a small nudge and begins to slide down his head. a) Determine the height at which the bug just begins to lose contact with his head in terms of the radius of his head. b) Determine the velocity of the bug at this point. c) Now assume the man's head instead accelerates horizontally to the left at g causing the bug to slide down and lose contact at some new height. Is this new height at which the bug loses contact with the head now greater or less than the height in part a). d) Assuming the scenario in part c), Show the angle that the bug loses contact with the man's head as measured with respect the vertical is about 17. Let g = 9.8 m/s.