Question

Four persons $K$ , $L$ , $M$ , $N$ are initially at the four corners of a square of side $d$ . Each person now moves with a uniform speed $v$ in such a way that $K$ always moves directly towards $L$ , L directly towards $M$ , $M$ directly towards $N$ , and $N$ directly towards $K$ . The four persons will meet at a time

• A. $\frac{d}{v}$
• B. $\frac{d}{2v}$
• C. $\frac{2d}{v}$
• D. The four persons will never meet

Answer 1

Answer: (A)

The velocity of K throughout the motion towards the centre of the square is $v$ $cos45^{\circ }$ and the displacement covered by this velocity will be KO.

$\therefore t=\frac{KO}{vcos45^{\circ }}=\frac{(\sqrt{2}\frac{d}{2})}{\frac{v}{\sqrt{2}}}=\frac{d}{v}$