Final answer:
To find the direction of the dog's resultant vector, we can break down its movement into components and use trigonometry to find the magnitude and direction of the resultant vector. The direction of the dog's resultant vector is 38.19° north of east.
Step-by-step explanation:
To find the direction of the dog's resultant vector, we can break down its movement into components. The first displacement is 3.5 m southeast, which means it is moving both south and east. The second displacement is 8.2 m at an angle of 30° north of east. Using the graphical method, we can add these displacements to find the resultant vector.
The first displacement can be split into components: 3.5 m south and 3.5 m east. The second displacement can be split into components: 8.2 m * cos(30°) east and 8.2 m * sin(30°) north.
Adding these components together, we get a total displacement of (3.5 m + 8.2 m * cos(30°)) east and (8.2 m * sin(30°) - 3.5 m) north. Using trigonometry, we can find the magnitude and direction of the resultant vector.
The magnitude is given by the formula: sqrt((3.5 m + 8.2 m * cos(30°))^2 + (8.2 m * sin(30°) - 3.5 m)^2). The direction is given by the formula: arctan((8.2 m * sin(30°) - 3.5 m)/(3.5 m + 8.2 m * cos(30°))). Rounding to the nearest hundredth, the direction of the dog's resultant vector is 38.19° north of east, so the correct answer is D) 38.19°.