Final answer:
To find how far Joaquin and Hugh are apart after two hours of sailing, calculate the distance each has sailed, break those distances into eastward, westward, and southward components, and then use the Pythagorean theorem to determine the total distance between them.
Step-by-step explanation:
To determine how far apart Joaquin and Hugh are after Joaquin has been sailing for two hours, we must calculate the distances each has traveled and then apply the Pythagorean theorem or use vector addition to find the distance between them. Joaquin sails 40 degrees south of east at 20 knots for two hours, which totals 40 nautical miles. For the direction, we can break this into eastward and southward components:
- Eastward: 40 * cos(40°) nautical miles
- Southward: 40 * sin(40°) nautical miles
Hugh starts half an hour later, so he sails for 1.5 hours at 25 knots, which totals 37.5 nautical miles in a direction 65 degrees west of south. Similarly, we can break this into southward and westward components:
- Southward: 37.5 * cos(65°) nautical miles
- Westward: 37.5 * sin(65°) nautical miles
Since Joaquin has no westward component and Hugh has no eastward component, the distance between them is a straight line that can be found using the Pythagorean theorem:
- ΔEast = Eastward component of Joaquin
- ΔWest = Westward component of Hugh
- ΔSouth = Southward component of Joaquin + Southward component of Hugh
Total distance D can be calculated as D = √((ΔEast²) + ((ΔWest + ΔSouth)²)). This calculation will yield the answer to how far apart Joaquin and Hugh are after the given period of time.