Final answer:
The student's question is about calculating the total distance a ship is from port after sailing along two different vectors. It requires vector addition and the application of trigonometry to find the ship's total displacement.
Step-by-step explanation:
The question involves calculating the distance a ship is from the port after sailing for a certain number of hours on different courses and at different speeds. This calculation is a problem of vector addition and displacement. To solve this problem, we need to break down the ship's movement into two separate vectors and then calculate the resultant vector, which represents the total displacement from the port.
The ship first sails for 4 hours on a course of 78° at 18 knots. The first vector's magnitude is the product of speed and time (4 hours × 18 knots). After altering course to 168°, it sails for 6 hours at 16 knots, resulting in a second vector with a magnitude of 6 hours × 16 knots. These vectors are then added using vector addition to determine the distance of the ship from the port.
The calculation may involve converting the angles to their respective components (north-south and east-west), multiplying each component by the duration and speed to find the displacement in each direction, and then using the Pythagorean theorem to find the total displacement from the port. If the angles are measured relative to north, then they must be adjusted to standard mathematical bearings before the components are calculated.