Question

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

• A. $500m$
• B. 500 $\sqrt{3}$ m
• C. $1000m$
• D. 1000 $\sqrt{3}$ m

Answer 1

The correct option is C $1000m$

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 takes the third turn at $D.$
Therefore, the magnitude of this displacement is
$AD=AG+GD$

$=500m+500m$

$=1000m$