Question

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
A. `d/vsec`
B. `(sqrt(2d))/vsec`
C. `d/(sqrt(2v))sec`
D. `d/(2v)sec`

Answer 1

Correct Answer - c
It is obvious from considerations of symmetry that at any moment of time all of the persons will be at the corners of square whose side gradually decreases (see fig.) and so will finally meet at the centre of the square O.

The speed of the each persons along the line joining his initial position and O will be `v cos 45=v//sqrt(2)`.
As each persons has displacement `d cos 45=d//sqrt(2)` to reach the centre, the four persons will meet at the centre of the square O after time.
`:. t=(d//sqrt(2))/(v//sqrt(2))=d/v`