Question

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, the displacement of the motorist at the third turn is

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

Answer 1

Answer: (C)

$1000\,m$

Answer 2

The path followed by the motorist is a regular hexagon $ABCDEF$ of side length $500\,m$ 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 $AD = AG + GD$ $= 500 \,m + 500 \,m$ $= 1000\, m$