Four person K,L,M and N are initally at the corners of a square of side of length d. If every person starts moving, such that K always heads towards L, L heads towards M, M heads directly towards N and N heads towards K, then the four perons will meet after

Answer

`d//v`

Explanation

The velocity of K throughout the
motion towards the centre of the square
is `v cos 45^@` and the displacement
covered by this velocity will be KO

`t = (KO)/(v cos 45^@) = (sqrt(2)d//2)/(v//sqrt2) = d/v`

Alternatively:
`vecv_(KN) = vecv_(K) - vecv_(N) = vecv_(k) + (-vecv_(N))` along the line
`KN = 0 + [-(-v)]=v`
Time taken for K and N to meet will be `d//v`.