4.10 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.

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Vishal Baghel | Contributor-Level 10

2 months ago

4.10

Since the motorist taking the 60° turn after every 500m, It will form a perfect hexagon of side 500m after 6 turns.

Suppose the motorist starts from point A. From A, turns 60° to reach B (first turn), then to C and so on.

1. At third turn, The magnitude of displacement = DG + GA = 500m + 500m = 1000m Total path length = AB + BC + CD = 500m +500m +500m = 1500 m

2. At sixth turn, When the motorist takes the 6th turn, he is at starting point A. Therefore,

The magnitude of displacement = 0Total path length = AB + BC + CD + DE + EF + FA = 500m

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