Answer :
Final answer:
The person is approximately 39.1 meters from where they started after walking 25 m west and 45 m at a 60° angle north of east. By breaking down the second displacement into its components and using vector addition followed by the Pythagorean theorem, we find the resultant displacement. So the correct option is d.
Explanation:
To solve the problem of how far a person is from where they started after walking a certain distance in specified directions, we can use vector addition. In this case, the person walks 25 m west and then 45 m at an angle of 60° north of east. The first step is straightforward, as walking west simply means we have a displacement vector pointing to the left (if we imagine a map with north at the top).
The second step requires breaking down the second vector into its northward and eastward components. The eastward component can be found using the cosine function, cos(60°) * 45 m, and the northward component using the sine function, sin(60°) * 45 m. After calculating these components, we can combine them vectorially with the original 25 m west displacement. The final step is to find the resultant vector's magnitude, which gives us the straight-line distance from the starting point, using the Pythagorean theorem.
- Calculate eastward displacement: cos(60°) * 45 m = 22.5 m.
- Calculate northward displacement: sin(60°) * 45 m ≈ 38.97 m.
- Combine with westward displacement: The net eastward displacement is 22.5 m - 25 m = -2.5 m (westward).
- Calculate the resultant displacement using the Pythagorean theorem: √((-2.5 m)² + (38.97 m)²) ≈ 39.1 m.
The approximate distance the person is from where they started is 39.1 m.
