Question

If six persons are at the corners of a regular hexagon of side $X$ move at a constant speed $V$. Each person maintains a direction towards the person at the next corner. The time, the persons will take to meet each other is

• A. $\frac{2X}{3V}$
• B. $\frac{2X}{V}$
• C. $\frac{X}{V}$
• D. $\frac{5X}{6V}$

Answer 1

Answer: (B)

$\frac{2X}{V}$

Velocity of one person towards another person (Relative) as seen from the second person be $V_1$.

Thus, $V_1=V-VCos{60}^0$ {i.e Velocity of A - Velocity of B along the line of motion of A}

$V_1=V-\frac{V}{2}=\frac{V}{2}$
$S=X$, (distance between the two person which needs to be covered)
Thus, $t=\frac{S}{V_1}=\frac{2X}{V}$