Four boys are standing at the four comers of a square ABCD of length of sideal. They simultaneously start running such that runs towards B, B runs towards C, C runs towards D and D runs towards A each with velocity . They will meet at after time given by :

Options

A. `(sqrt(2)a)/(v)`
B. `a/v`
C. `(a)/(sqrt(2)v)`
D. `sqrt(a//v)`

Answer

b

Explanation

The four person will meet at the centre O of the square of side a. They describe curvilinear pathh as they have to face each other always.
Net displacement is `A_(0)=(1)/(2)AC`
`A_(0)=(1)/(2)sqrt(a^(2)+a^(2))=(1)/(2)sqrt(2a)=(a)/(sqrt(2))`

Component of velcoity v along AO is
`=v cos 45^(@) =(V)/(sqrt(2))`
`:. `Time taken` =("displacement")/("velocity")=((a)/sqrt(2))/((v)/(sqrt(2)))=(a)/(v)`