Question

Four persons $A,B,C$ and $D$ at the corners of a square of side $X$ start moving at a constant speed $V$. Each person maintains a direction towards the person at the next corner. The time the persons take to meet each other is

• A. $\frac{2X}{3V}$
• B. $\frac{X}{3V}$
• C. $\frac{X}{V}$
• D. $\frac{3X}{4V}$

Answer 1

The correct option is C $\frac{X}{V}$

The motion of $A,B,C$ and $D$ is shown in the figure. They will eventually meet at the center $O$.

This means the displacement of $A$ will be $AO$. And his velocity along $AO$ will be
$V\cos \theta =V\cos {45}^{\circ }=V/\sqrt{2}$
Now using Pythagoras theorem on triangle $△AEO$,
$AO=X/\sqrt{2}$
Therefore, time taken to reach $O$ from $A$ will be,
$t=\frac{AO}{V\cos \theta }=\frac{X/\sqrt{2}}{V/\sqrt{2}}=\frac{X}{V}$
This will be the time taken for all $A,B,C$ and $D$ to meet each other.