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 the path skate?

Answer 1

As a very first step, one could read the question and hence note down the important points given in it. Also analyse the given figure and also recall the definition of displacement and also give how it is different from the distance covered. Thereby, find the answer to the question accordingly.

Complete step-by-step solution:
In the question, we are given two girls who are skating on a circular ice ground that has a radius of 200m. All three start from a point P on one edge to point Q on the other edge by three different paths A, B and C. We are supposed to find the magnitude of the displacement vector in each of the given paths.
We could define displacement as the shortest distance between the initial and final positions of a particle. We see that for all the three cases the initial and final positions are the same and hence shortest distance, i.e., the displacement would be the diameter of the circular ground.
$\overrightarrow{PQ}=2\times r=2\times 200=400m$
Hence, we also found that the displacement is the actual path taken by the skater B.

Note: One may recall that displacement is not a path dependent quantity while distance is. Though the displacement of the three skaters is the same, the distance covered by three of them is different. Displacement is a vector quantity that has both magnitude and direction while distance is a scalar quantity with only direction.