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On an open ground, a motorist follows a track that turns to his left by an angle of 600 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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Answer» -On an OPEN ground, a motorist FOLLOWS a track that turns to his left by an angle of 600 after every 500 m.To Find :-Compare the magnitude of the displacement with the total path length covered by the motorist in each case.Solution :-Given that,The path followed by the motorist is a regular hexagon with side 500 m.Let us consider,Let the motorist start from POINT P.The motorist takes the third turn at S.Magnitude of the displacement = PS = PV + VSSubstituting them,Now,Total path length = PQ + QR + RSBy substituting,The motorist takes the 6TH turn at point P, which is the starting point.Then,Magnitude of displacement = 0Total path length = PQ + QR + RS + ST + TU + UPSubstituting their values,The motorist takes the eight turn at point R.Magnitude of displacement = PRBy substituting,Therefore, the magnitude of displacement is 866.03 m at an angle of 30° with PR.Total path length = Circumference of the hexagon + PQ + QRSubstituting them, |
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