On an open ground, a motorist follows a track that turns to his left by an angle of $60^{\circ}$ aft

Question

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

Professor PC Thomas Classes · Answer

(c) : The path followed by the motorist is a regular hexagon $A B C D E F$ of side length 500 m as shown in the figure. Let the motorist start from $A$ and takes the third turn at $D$. Therefore, the magnitude of this displacement is $A D=A G+G D=500 \mathrm{~m}+500 \mathrm{~m}=1000 \mathrm{~m}$