Question

Four persons A,B,C and D initially at the corners of a square of side d. If every person starts moving with same soeed v such that each one faces the other always, the person will meet after time

Answer 1

This is an excellent question! 

Intuitively, it may seem like the four people will never meet, because the person they are moving towards is always moving away from them. The key is that while the person they are moving towards is moving, they are not actually moving away from the person chasing them. In fact, the person moving away will always move perpendicular to the line between them and the person chasing them, so they never get further away from their pursuer. On the other hand, the person chasing them is always moving towards them at speed v. Therefore, the distance between these two people decreases at speed v, and the time it takes for them to meet is dv.dv..

For the more mathematically inclined, this may not seem like much of a proof, so here is a way to show this with a little bit of calculus:

First, let's look at what would happen if all of the people were to move in their initial direction (set only by the initial positions of K,L,M,N) for a time t=Δt

Answer 2

Answer: ​t=d/v

Explanation:★ 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/  root 2

​Distance covered =  d/  root 2

​Time taken t =d/  root 2  /v/  root 2

​t=d/v

HOPE YOU ARE SATISFIED

SEE THE IMAGE FOR UNDERSTANDING EQUATION