Final answer:
The motion of a boat across a river is affected by both its own velocity and the current's velocity. To reach a point directly east across a swiftly flowing river, the captain must steer the boat to head upstream at an angle compensating for the directional influence of the river's current. The exact required angle cannot be determined without additional specifics or the referenced figures.
Step-by-step explanation:
Understanding the Motion of a Boat on a River
When considering the motion of a boat on a river, it is crucial to analyze the effects of both the boat's velocity and the river's current. Our situation involves a river flowing from southwest to northeast at a velocity of 7.1 m/s and a boat that can move at 13 m/s. The captain wants to reach a point directly east of the current location, which requires navigating the boat across the flow of the river.
To achieve this, the boat must steer at an angle that compensates for the river's downstream current. Since the river's velocity is not negligible compared to the boat's speed, the direction the boat must head towards is affected significantly—less than 45° in relation to the shore. Using vector addition, where each component represents part of the total motion, we can calculate the angle and direction for the boat to aim to reach the desired destination on the opposite shore.
With the information given, the boat must head across the river. Accounting for the river's downstream current, the resultant velocity will be more significant than either the individual speed of the boat or the river. However, without the exact figures or the ability to view the referred figures (3.43, 3.44, 3.47, and 3.40) from the question, providing the precise correct option in the final answer would be assuming details not provided in the question. In general, if the velocity of the river is larger than the boat's speed, the boat will be swept downstream. Therefore, it should head upstream to some degree to compensate.