When analyzing motion, especially in two dimensions, breaking down a vector into its components helps simplify the problem. Each component represents the vector's influence in one particular direction, typically aligned with the coordinate axes, like north-south and east-west.
In the ferry scenario, the velocity vector of the person can be split into two components:
- The northward velocity component \(v_y = 6.2 \; \text{m/s}\)
- The eastward velocity component \(v_x = 1.1 \; \text{m/s}\)
These components are perpendicular to each other and can be individually measured in terms of their magnitude and direction.
Understanding velocity components is crucial because it allows for easy calculation of the resultant velocity through vector addition. By solving for each component separately, we gain insights into how each direction contributes to the overall motion. This technique is invaluable in physics to simplify complex three-dimensional motion into more manageable two-dimensional problems.