Final answer:
The magnitude and direction that Andrew must travel are determined by subtracting his initial displacement vector from the treasure's location vector. The process involves breaking down into components and calculating the resultant vector, but cannot be completed without further trigonometric values.
Step-by-step explanation:
To find the magnitude and direction Andrew must travel to get to the treasure after his first displacement, we start by analyzing his initial movement. Andrew travels at a speed of 12 m/s in the direction [W45N] for 7 seconds. The distance covered in this initial leg would be speed multiplied by time, which equals 12 m/s * 7 s = 84 meters. The displacement vector for this initial movement will have both westward and northward components because of the 45-degree angle from the west towards the north.
Since the final treasure location is 250m [S33W], we can consider the treasure’s position as another vector from the starting point. To determine the second leg of Andrew’s journey, we need to find the vector that will sum with his initial displacement to equal the treasure’s vector. This can be accomplished by vector subtraction: Treasure Vector - Initial Displacement Vector = Required Displacement Vector for the second leg.
Unfortunately, without more specific trigonometric values or a graphical representation, we cannot provide an exact numerical answer. However, the process would involve breaking down both the initial displacement and the treasure’s location into their north/south and east/west components, subtracting appropriately, and then calculating the resultant vector's magnitude and direction.