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. 3.19. What is the magnitude of the displacement vector for each? For which girl is this equal to the actual length of the path skated?Figure 3.19

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.

Radius of the ground = $200\;m$
Diameter of the ground = $2\times 200$ = $400\; m$

Hence, the magnitude of the displacement for each girl is $400\; m$. This is equal to the actual length of the path skated by girl B.