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 $M$, $M$ directly towards $N$, and $N$ directly towards $K$. The four persons will meet at a time _________.

Answer 1

R.E.F image

$★$ Each person moves with constant speed towards

the other but its velocity changes continuously.

$★$ They will meet at the center Finally.

$★$ After every Unit time they will from smaller square

Component of Velocity Towards center $=vcos45$

$=v/\sqrt{2}$

Distance covered $=\frac{\sqrt{2d}}{2}\frac{\left(diagonal\right)}{2}$

$=d/\sqrt{2}$

Time taken t $=d/\sqrt{2}/v/\sqrt{2}$

$t=d/v$ Ans