Final Answer:
a) Distance traveled:
South: 104.9 nautical miles
West: 58.2 nautical miles
b) Ship's position at 7:00 PM:
Bearing: 270° West
Distance from port: Approximately 113.5 nautical miles
Step-by-step explanation:
a) Distance traveled:
Total distance: The ship sails for 6 hours at 20 knots, so the total distance traveled is 6 hours * 20 knots/hour = 120 nautical miles.
Bearing components: We can use trigonometry to find the north-south and east-west components of the distance traveled.
South: Sin(24°) * 120 nautical miles ≈ 104.9 nautical miles south
West: Cos(24°) * 120 nautical miles ≈ 58.2 nautical miles west
b) Ship's position at 7:00 PM:
Westward distance: Since the ship sails due west for 1 hour, it covers an additional 20 nautical miles westward.
Resultant distance: Combining the south and west components, the total distance from the port is √(104.9² + (58.2 + 20)² ≈ 113.5 nautical miles.
Bearing: The ship's final direction is due west, which is 270° from the port.
Note: This is a simplified solution assuming the Earth is flat. In reality, Earth's curvature would slightly affect the calculations, but the general approach remains the same.