question_answer 10)

On an open ground, a motorist follows a track that turns to his left by an angle of 60° after every 500 m. Starting from a given turn, specify the displacement of the motorist at the third, sixth and eighth turn. Compare the magnitude of the displacement with the total path length covered by the motorist in each case. 

Answer:

                As shown in Fig. 4.103, suppose motorist starts from point A.     Fig. 4.103   Clearly, he will follow the hexagonal path ABCDEFA. The orders of the turns taken by him are indicated at the vertices of the hexagon. (i) At the third turn, the motorist will be at D. The magnitude of displacement  will be             . The direction of  is 60° left of the initial direction AB. Total path length . (ii) At the sixth turn, the motorist comes back to the starting point A, so magnitude of displacement is zero. Total path length   . (iii) At the eighth turn, the motorist will be at C. The magnitude of his displacement  is                   . The direction of  is 30° left of the initial direction . Total path length = 500 x 8 = 4000 m = 4 km.