A sailboat departs from a mooring buoy that is taken as the origin of an xy-coordinate system (+x east, +y north). The boat follows three successive legs:
• Leg 1: 4.0km on a heading 30∘ north of east.
• Leg 2: 3.0km due south.
• Leg 3: 2.0km on a heading 45∘ west of north.
(a) For each leg, calculate the east (x) and north (y) components of the displacement. Organize your results in a clear table.
(b) Determine the components of the boat’s net displacement relative to the mooring buoy.
(c) Compute the magnitude of the net displacement and the bearing (angle measured clockwise from north) of the boat’s final position relative to the buoy.
(d) The captain wishes to return directly to the buoy along a straight line at an average speed of 5.0kmh−1. Estimate the time required for this direct return trip.