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Question: On an open ground, a motorist follows a track that turns to his left by an angle of \(60^{o}\)after ...

On an open ground, a motorist follows a track that turns to his left by an angle of 60o60^{o}after every 500 m. Starting from a given turn, the displacement of the motorist at the third turn is

A

500 m

B

5003m500\sqrt{3}m

C

1000 m

D

10003m1000\sqrt{3m}

Explanation

Solution

The path followed by the motorist is a regular hexagon ABCDEF of side length 500m as shown in the figure. Let the motorist starts from A and taken the third turn at D.

Therefore, the magnitude of this displacement is

AD = AG + GD = 50 m + 500 m = 1000 m