Final answer:
The problem is related to determining the resultant velocity and direction of a boat in a river current, which is solved using vector addition. This requires adjusting the boat's heading to compensate for the influence of the current in order to reach the intended target directly across the river.
Step-by-step explanation:
The question involves vector addition to determine the resultant velocity and direction of a boat traveling across a river with a current. When a boat moves across a river, its velocity relative to the shore is affected by the river's current. This is a classic physics problem that can be solved by using vector addition, often requiring the use of trigonometry or graphical methods to find the resulting speed and direction.
For example, if a boat moves at a certain speed in still water and then encounters a current, the actual path and speed of the boat (its resultant velocity) will be a combination of its speed through the water and the speed and direction of the current. This combination is found through vector addition, accounting for the magnitudes and directions of both vectors. The process usually involves breaking down the vectors into their horizontal and vertical components, summing those components, and then calculating the magnitude and angle of the resultant vector from the sums of the components.
Determining the correct heading of the boat to compensate for the river's current requires a calculation to ensure the desired path across the river is maintained. The heading must be adjusted upstream to offset the current's influence. Without this adjustment, the current would carry the boat downstream, causing it to miss the intended target directly across the river.