Circular Ice Skating Displacement
Problem Statement
Three girls skating on a circular ice ground of radius 200 m start from point P and reach point Q diametrically opposite to P following different paths. What is the magnitude of the displacement vector for each? For which girl is this equal to the actual length of path skated?
Skater A: Straight line
Displacement:
400 m
Path length:
400 m
Skater B: Semicircle
Displacement:
400 m
Path length:
628.32 m
Skater C: Quarter circle
Displacement:
400 m
Path length:
314.16 m
Skater D: Three quarter circle
Displacement:
400 m
Path length:
942.48 m
Key Observations:
1. All skaters have the same displacement magnitude (400 m) since they all travel from P to Q.
2. Only Skater A (straight line) has path length equal to the displacement magnitude.
3. Displacement depends only on initial and final positions, while path length depends on the actual route taken.
