Question

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 .............. .

Answer 1

Correct Answer - D
The relative velocity of `K` w.r.t `L` along the line `KL` is `vec(v)_(KL) = vec(v)_(K) - vec(v)_(L) = vec(v)_(K)+(-vec(v)_(L))`
` = v`
(`because` the component of velocity of `L ` along `KL` is zero )
The displacement of `K` till `K` and `L` meet is `d`.
`:.` Time taken for `K` and `L` to meet will be `= (d)/(v)`