Question

Six persons of same mass travel with same speed along a regular hexagon of side ${}^{\prime }{d}^{\prime }$ such that each one always faces the other. After how what will they meet each other?

• A. $\frac{d}{u}$
• B. $\frac{2d}{3u}$
• C. $\frac{2d}{u}$
• D. $d\sqrt{3}u$

Answer 1

The correct option is C $\frac{2d}{u}$

Given :

Particle $A$ moves towards $B$ with a speed $u$ m/s.

Let us calculate the speed of $B$

:$B$ is also moving with velcoity $u$ along $BC$ direction.

Hence velocity component along $BC:$

$u\cos {60}^{\circ }=\frac{u}{2}$

Relative speed of particle $A$ with respect $B=u-\frac{u}{2}=\frac{u}{2}$.

To travel a distance $d$ , time taken by the particle:

Time$=\frac{Distance}{Speed}=\frac{d}{\left(\frac{u}{2}\right)}=\frac{2d}{u}$