Final answer:
The distance from the starting point is approximately 30.8 meters, and the compass direction of the displacement vector is approximately 35.54° west of north.
Step-by-step explanation:
To determine how far you are from your starting point after walking 18.0 m straight west and then 25.0 m straight north, we can use the Pythagorean theorem. This theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this scenario, we have a right-angled triangle with the sides being 18.0 m and 25.0 m.
First, we calculate the distance:
- Distance2 = West2 + North2
- Distance2 = (18.0 m)2 + (25.0 m)2
- Distance2 = 324 m2 + 625 m2
- Distance2 = 949 m2
- Distance = √949 m2
- Distance ≈ 30.8 m
The displacement is about 30.8 meters from the starting point.
To find the direction of your displacement, you can use trigonometry. The angle θ with respect to the north can be found using the tangent function, which is the ratio of the opposite side over the adjacent side:
- tan(θ) = West / North
- tan(θ) = 18.0 m / 25.0 m
- θ = arctan(18.0 m / 25.0 m)
- θ ≈ arctan(0.72)
- θ ≈ 35.54°
The compass direction of the displacement vector is approximately 35.54° west of north. The displacement vector itself can be written as R = 30.8 m at 35.54° west of north.