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

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√3 m (C) 1000 m (D) 1000√3 m

Tardigrade Admin · Accepted Answer

The path followed by the motorist is a regular hexagon ABCDEF of side length 500 m as shown in the figure. <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/c93df832df1cf0a3c2166127d91ecedb-.jpeg" /> 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

Q. On an open ground, a motorist follows a track that turns to his left by an angle of $6 0^{°}$ after every $500 m$ . Starting from a given turn, the displacement of the motorist at the third turn is

$500 m$

$5003 m$

$1000 m$

$10003 m$

The path followed by the motorist is a regular hexagon $A BC D EF$ 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
$A D = A G + G D$
$= 500 m + 500 m$
$= 1000 m$

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

500m

5003​m

1000m

10003​m