Final answer:
To calculate the magnitude of displacement for Samantha's walk, one must recognize the semi-circular path as having a displacement equal to its diameter of 4 meters, forming a right-triangle with the 4-meter horizontal path, which results in a total displacement of 5.66 meters.
Step-by-step explanation:
The magnitude of displacement for a person walking along a given path is the shortest distance from the start to the finish point, which is a straight line connecting these two points. To calculate displacement, one must consider the path in terms of vector addition. For a semi-circle with a radius of 2 meters followed by a straight horizontal path of 4 meters, the displacement is calculated using the radius and the straight line to form a right-angled triangle.
In this case, the semi-circle creates a displacement of 4 meters (the diameter) directly opposite the initial starting position. When coupled with the additional 4 meters of the horizontal path, the total displacement is calculated using the Pythagorean theorem:
- Displacement = √(horizontal distance² + (semi-circle displacement)²)
- Displacement = √(4m² + 4m²)
- Displacement = √(16m² + 16m²)
- Displacement = √(32m²)
- Displacement = 5.66 meters (to two decimal places).