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Question
Three girls skating on a circular ice ground of radius 200 m start from a point P on the edge of the ground and reach a point Q diametrically opposite to P following different paths as shown in Fig. What is the magnitude of the displacement vector for each? For which girl is this equal to the actual length of path skated?
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Solution
Step 1: Find displacement for each girl.
As given radius of skating ground = 200 m.
Initially three girls are at point P and finally at Q, that means initial and final position of all girls are same.
Hence displacement will be same.
Displacement =−−→PQ
Magnitude of displacement = PQ
= 2 (Radius of skating ground)
=2×200=400 m.
Step 2: Compare displacement with path travelled by girls.
As girl B moves along diameter of circular track so, displacement for girl B is equal to the actual path length skated.
Final Answer:
The magnitude of the displacement vector for each is 400 m.
This displacement is equal to the actual length of path skated by girl B.
As given radius of skating ground = 200 m.
Initially three girls are at point P and finally at Q, that means initial and final position of all girls are same.
Hence displacement will be same.
Displacement =−−→PQ
Magnitude of displacement = PQ
= 2 (Radius of skating ground)
=2×200=400 m.
Step 2: Compare displacement with path travelled by girls.
As girl B moves along diameter of circular track so, displacement for girl B is equal to the actual path length skated.
Final Answer:
The magnitude of the displacement vector for each is 400 m.
This displacement is equal to the actual length of path skated by girl B.
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