Final answer:
The question requires knowledge of coordinate system conversions and vector components. By using trigonometric identities, the x and y components of vectors can be expressed, and polar coordinates can be converted to Cartesian coordinates for further calculations.
Step-by-step explanation:
This question revolves around the conversion of coordinates from one system to another and finding component vectors based on angle and magnitude. To express the x and y-components of a vector, we use the equations Ax = A cos(θ) and Ay = A sin(θ), where A is the magnitude of the vector and θ is the direction or global angle.
For Cartesian coordinates conversion from polar coordinates with a radius (r) and angle (θ), the formulas are x = r cos(θ) and y = r sin(θ). Applying these to the given polar coordinates (47/3, 5.50 m) we obtain the Cartesian coordinates.
For two points with polar coordinates P₁ (2.500 m, π/6) and P₂ (3.800 m, 27/3), we convert each to Cartesian coordinates and use the distance formula d = √((x₂ - x₁)² + (y₂ - y₁)²) to determine the distance between them.
Using the initial point as a reference helps answer questions about positions and displacement relative to that point or another reference point.