Final answer:
The stand-on vessel should maintain its course and speed while being overtaken by the give-way vessel in navigational contexts. Physics principles also apply to the scenarios described, calculating relative motion in water currents.
Step-by-step explanation:
The student's question appears to be related to the rules of navigation and physics principles concerning the motion of vessels in water currents. However, the excerpts provided seem to mix narrative elements with physics problems. In the context of navigational rules, the phrase that fits the blank in 'The boat being passed is the ____ vessel' would likely be the 'stand-on' vessel, according to maritime rules.
This means it should maintain its course and speed. The boat that is overtaking, or the one trying to pass, would be the 'give-way' or 'burdened' vessel, and it is responsible for safely passing the stand-on boat. Regarding physics, the examples given illustrate problems of relative motion, such as the calculation of the velocity of a boat with respect to Earth when considering both its own velocity and the current of a river.
In the context of the narrative elements, it is important to provide assistance with interpreting the text rather than offering a strict navigational or physics answer. This distinction should be clear in communication with the student to maintain a focused and effective tutoring session.