Final answer:
To find the displacement and compass direction after walking 18.0 m west and then 25.0 m north, use the Pythagorean theorem to calculate the magnitude of the displacement and trigonometry to find the direction relative to north.
Step-by-step explanation:
To solve the problem of determining how far you are from your starting point after walking 18.0 m straight west and then 25.0 m straight north, and finding the compass direction of a line connecting your starting point to your final position, you can use the Pythagorean theorem and trigonometry, as these displacements can be represented by vector additions.
The first step is to recognize that walking 18.0 m west and 25.0 m north forms a right triangle with the legs being the distances walked in each direction. So, to find the total displacement (the hypotenuse of the triangle), you use the Pythagorean theorem: displacement = √(18.0^2 + 25.0^2).
To find the compass direction of this displacement vector, you calculate the angle between the north direction and the displacement vector using trigonometry, specifically the arctangent function: angle = arctan(opposite/adjacent), where opposite is the westward displacement (18.0 m) and adjacent is the northward displacement (25.0 m).
After calculating these values, you get the total displacement and its direction from north. The magnitude of the displacement vector is the direct distance between the starting point and the final position, and the compass direction can be expressed relative to north (e.g., degrees west of north).