Question

A scooterist follows a track on a ground that turns to his left by an angle 60${}^0$ after every 400 m. Starting from the given point displacement of the scooterist at the third turn and eighth turn are :

• A. $800m;0m$
• B. $800m,800\sqrt{3}m$
• C. $800m;400\sqrt{3}m$
• D. $800;800\sqrt{3}m$

Answer 1

Answer: (C)

$800m;400\sqrt{3}m$

Let $\overline{x_1},\overline{x_2},\overline{x_3},.....\overline{x_8}$ be the positions of scooterist after $1^{st},2^{nd},3^{rd}......,8^{th}$ turn respectively.

Thus its motion can be visualized as hexagon inscribed in circle of radius $400m$.

Let $\overline{x_0}$ be its initial position.

$\therefore$ After $3^{rd}$ turn

$x_3-x_0=800m$

After $8^{th}$ turn

$x_0-x_2=800\cos {30}^0=400\sqrt{3}m$