Question

Three persons $P,Q$ and $R$ are at three corners of an equilateral triangle of each side $a$. They start moving simultaneously with velocity $V$ such that $P$ always moves towards $Q$, $Q$ always moves towards $R$ and $R$ always moves towards $P$. After what time they would meet each other at $O$ ?

• A. $\frac{a}{V}$
• B. $\frac{2a}{3V}$
• C. $\frac{2a}{\sqrt{3}V}$
• D. $\frac{2a}{V}$

Answer 1

The correct option is B $\frac{2a}{3V}$

The three persons follow curvilinear paths to meet at the centroid $O$ of triangle.
Displacement $PO=QO=RO=\frac{a}{\sqrt{3}}$

Velocity component along the displacement
$=V\cos {30}^{\circ }=\frac{V\sqrt{3}}{2}$
$\therefore t=\frac{\frac{a}{\sqrt{3}}}{\frac{V\sqrt{3}}{2}}=\frac{2a}{3V}$