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

Options

A. `d/v`
B. `(sqrt2d)/v`
C. `d/(sqrt2v)`
D. `d/(2v)`

Answer

A

Explanation

The four persons K,L,M and N will meet at i.e ., the centre of the diagonal of the square KLMN. The person K will travel a distance KO, with velocity along KO = Here, KO `= v cos 45^@`
`=v/sqrt2`
Here , KO `= d cos 45^(@) = d/ sqrt2`

`:.` Time of meeting , `t = (distance) / (velocity) = (d//sqrt2)/(v//sqrt2)=d/v`