Question

Three girls skating on a circular ice ground of radius $200m$ 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 skate ?

Answer 1

Displacement is given by the minimum distance between the initial and final positions of a particle. In the given case, all the girls start from point P and reach point Q. The magnitudes of their displacements will be equal to the diameter of the ground.
The radius of the ground $=200m$
Diameter of the ground$=2\times 200=400m$
Hence, the magnitude of the displacement for each girl is $400m$. This is equal to the actual length of the path skated by girl B.