Answer :
The magnitude of the displacement required to bring the skater back to her starting point is approximately 78.3 meters.
We can solve this problem by breaking down the skater's movements into their east and north components and then using the Pythagorean theorem to find the magnitude of the final displacement.
1. Decompose the movements:
- Southwest (22.3 m):
- This movement has a negative east component (since south is "down" on a coordinate plane) and a negative north component.
- We can estimate the east component using the sine function:
- East component (approx.) = -22.3 m * sin(180° + 45°) ≈ -15.77 m (negative due to southwest direction)
- The north component is also negative: North component = -22.3 m * cos(180° + 45°) ≈ -15.77 m
- East (44.6 m):
- East component = 44.6 m (entirely east)
- North component = 0 m (no north or south movement)
- 48.1° north of east (66.9 m):
- We can estimate the east component using the cosine function:
- East component (approx.) = 66.9 m cos(48.1°) ≈ 44.51 m
- North component = 66.9 m sin(48.1°) ≈ 51.20 m
2. Sum the components:
- Total east component = (-15.77 m) + 44.6 m + 44.51 m ≈ 72.34 m
- Total north component = (-15.77 m) + 0 m + 51.20 m ≈ 35.43 m
3. Find the magnitude of the displacement:
- Apply the Pythagorean theorem:
- Displacement magnitude = √(East component² + North component²)
- Displacement magnitude ≈ √(72.34² m² + 35.43² m²) ≈ 78.3 m
Therefore, the magnitude of the displacement required to bring the skater back to her starting point is approximately 78.3 meters.
Q-An ice skater skates 22.3 m southwest, then 44.6 m east, and finally 66.9 m in a direction 48.1 â—¦ north of east. find the magnitude of the displacement required to bring the skater back to her starting point. answer in units of m.
