scalars and vectors - 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. 4.20. What is the magnitude of the displacement vector for each ? For which girl is this equal to the actual length of path skate ?

Grigori (last edited 4 months ago) (Student, UG2 Grade)

Displacement is defined as the shortest distance between a particle's initial and final positions.

Step 1: Calculating the magnitude of the displacement

Given that

Radius of the circular ice ground r = 200 m

Girls began skating at point P and moved to point B.

Magnitude of the displacement for each girl is equal to the diameter of the circular ice ground since it is the shortest distance between P and Q

Diameter of the circular ice ground = 2* Radius of the circular ice ground

D = 2 * 200

D = 400 m

Hence, magnitude of the displacement for each girl D = 400 m

Step 2: Find the girl who travelled through the actual displacement

Magnitude of the displacement is the exact length of the route that girl B skated.