Question

Three particles $P,Q$ and $R$ are at rest at the vertices of an equilateral triangle of side $s$ . Each of the particles starts moving with constant speed $vm{s}^{-1}.P$ is moving along $PQ,Q$ along $QR$ and $R$ along $RP$ . The particles will meet each other at time $t$ given by

• A. $\frac{s}{v}$
• B. $\frac{3s}{v}$
• C. $\frac{3s}{2v}$
• D. $\frac{2s}{3v}$

Answer 1

Answer: (D)

The velocity component towards centroid $O$ of
triangle $=v\cos \theta$
$=v\cos 30^{\circ }=\frac{\sqrt{3}}{2}v$
Distance $PO=-\frac{2}{3}$ of altitude
$=\frac{2}{3}\times \frac{\sqrt{3}}{2}s=\frac{1}{\sqrt{3}}s$
$\Rightarrow$ Time $=\frac{\text{Distance}}{\text{Speed}}$
$=\frac{\frac{1}{\sqrt{3}}s}{\frac{\sqrt{3}}{2}v}$
$=\frac{2}{3}\cdot \frac{s}{v}$