Four persons K,L,M,N are initially at the four corners of a square of side d. Each person now moves with a uniform speed v in such a way that K always moves directly towards L, L directly towards M, M directly towards N, and N directly towards K. The four persons will meet at a time............. .

Options

A. ` l//2 v`
B. sqrt 2 l //v`
C. `l//sqrt 2 v`
D. ` l//v`.

Answer

D

Explanation

At the start, the velocity fo athlete at (A) is ` (v) along (AB). The componet of this velocity along
` AO= v cos ` 45^@ = v sqrt 2)`.
Distance ` AO = 1/2 AC= 1/2 ( sqrt (l^2 + l^2) = l/( sqrt 2)`
Time taken by athletes to meet at (O) is
` t = (distance AO)/( speed along AO) = ( l//sqrt 2)/( v //sqrt 2) = l/v`.