Final answer:
A boater's speed of operation varies according to the boat's velocity relative to water and water's velocity relative to the riverbank. It involves calculating these factors to determine the resultant speed, as well as direction for crossing a river or calculating the speed relative to an observer on the shore.
Step-by-step explanation:
A boater's speed of operation will vary according to several factors, including the velocity of the boat relative to the water and the water's velocity relative to the riverbank. For example, if a boat can be rowed at 8.0 km/h in still water and the river is moving at 3.0 km/h relative to the shore, the resultant velocity downstream would be the sum of these two speeds when moving downstream. Conversely, when rowing upstream, the speed of the river will subtract from the boater's speed.
The direction the boat must be aimed to cross straight might involve calculating an angle depending on the speed and direction of the river flow. For example, the boat might need to aim at an angle of 26.6° relative to a line drawn across the river to compensate for the current. This involves understanding vector addition and the relationship between the boat's velocity, the water's velocity, and the desired resultant velocity.
When considering the speed of boats relative to the riverbank, such as two speedboats traveling in opposite directions with speeds of 4.0 m/s and 5.0 m/s observed from the bank, calculations would involve understanding relative motion to determine both the speed of the boats relative to the water and the speed of the water relative to the shore.