Final answer:
Boat A and Boat B's captains will see each other moving away at the same speed but in opposite directions due to relative velocity. In a river scenario, observers on shore would see each boat moving at different speeds, influenced by the river's current. Determining these speeds involves classical relativity and relative velocity principles.
Step-by-step explanation:
If Boat A and Boat B are traveling at constant speeds in opposite directions and pass each other, each captain will observe the other boat's motion relative to their own frame of reference. This situation involves concepts from classical relativity and relative velocity, key topics in physics. The captain of Boat A will see Boat B moving away at a certain velocity, and conversely, the captain of Boat B will see Boat A moving away at the same velocity but in the opposite direction. Their descriptions regarding the motion will be symmetric but in opposite directions, analogous to how dropping binoculars from a moving ship's mast is seen differently by observers on the ship and on shore, yet the outcome is the same.
In the context of the moving river, where two speedboats travel with the same speed relative to the water but opposite to each other, observers on the riverbank would measure different velocities for each boat due to the river's current. Such calculations would again involve analyzing relative velocities to determine both the speed of the boats and the speed of the river flow relative to the stationary shore.