Question

Four persons $P,Q,R$ and $S$ are initially at the four corners of a square side $d$. Each person now moves with a constant speed $v$ in such a way that $P$ always moves directly towards $Q,Q$ towards $R,R$ towards $S,$ and $S$ towards $P$. The four persons will meet after time

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

Answer 1

The correct option is B $\frac{d}{v}$

Here, velocity components will be $v\cos 45=\frac{v}{\sqrt{2}}$

And, displacement will be $\frac{d}{\sqrt{2}}$

So time taken will be

$t=\frac{d}{v}$

$=\frac{\frac{d}{\sqrt{2}}}{\frac{v}{\sqrt{2}}}=\frac{d}{v}$