Question

Four persons $A,B,C$ and $D$ at the corners of an square of side $X$ move 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. $\frac{2X}{V}$
• C. $\frac{X}{V}$
• D. $\frac{3X}{4V}$

Answer 1

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


Each particle is moving in a direction perpendicular to that of the particle following it.
Relative velocity of particle $1$ along direction of particle $2$ is $V_{12}=V-0$
Relative distance of particle $1$ w.r.t $2$ $=X$
Time taken by particle $1$ to reach particle $2$ is $t=\frac{X}{V}$
Hence the correct answer is option (c)