Final answer:
The total distance from the starting point is approximately 30.8 m, and the direction of the displacement vector is 54.0° north of west.
Step-by-step explanation:
To determine how far you are from the starting point after walking 18.0 m straight west and then 25.0 m straight north, you can use the Pythagorean theorem. In this context, the displacement vectors are perpendicular to each other, therefore:
- The displacement to the west is represented as -18.0 m along the x-axis (since west is the negative direction on the x-axis).
- The displacement to the north is represented as 25.0 m along the y-axis.
To find the total displacement vector, we calculate the magnitude:
√((-18.0 m)² + (25.0 m)²) = √(324 + 625) = √(949) ≈ 30.8 m
To find the direction of the displacement vector, we use the tangent of the angle, θ:
tan(θ) = opposite/adjacent = 25.0 m / 18.0 m
θ = arctan(25.0 m / 18.0 m) ≈ 54.0°
Since we have moved west and north, the direction of the displacement is 54.0° north of west. The correct answer from the choices is closest to option (a): approximately 30.8 m; 30.8 m, 54.0° north of west.