Final answer:
Both boats should turn to their right to avoid a collision. For a boat to cross a river with a current, it must aim at an angle that compensates for the river's flow, such as 22.6° south of east if the river flows from southwest and the boat aims to reach directly east.
Step-by-step explanation:
When two boats meet head-on, nautical rules, known as Rule of the Road, require both boats to turn to their right (starboard side) to avoid a collision. This is akin to vehicle traffic rules on a two-way road where both vehicles would also move to the right to pass each other safely. In terms of crossing a river and dealing with current, a different scenario is presented.
The boat must account for the river's velocity to ensure it reaches the intended point on the opposite shore. If the river's current flows from southwest to northeast at 7.1 m/s, and the boat has a velocity of 13 m/s, the boat should aim in a direction that compensates for the river's current to achieve a resultant velocity that allows the boat to reach the target directly east.
A useful physics principle here is vector addition where velocities are treated as vectors. You add the velocity of the boat (Vboat) and the velocity of the river (Vriver) to determine the resultant velocity. As mentioned in the available reference information, if the velocities were equal, the direction of the total velocity would have been 45°.
For this particular problem with the boat and river velocities given, the boat should aim in a direction of 22.6° south of east, allowing the boat to travel directly east across the river despite the northeast-flowing current.