Two bodies are moving as shown in figure. Body A is moving in horizontal direction with velocity 4 m/s. Body B is moving at an angle of $6 0^{\circ}$ with horizontal. The velocity (in $m / s$ ) of body B so that velocity of A with respect to $B$ is minimum is

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v A ​ = 4 i , v B ​ = v ( cos 60 i + sin 60 j ) . Relative speed squared: ( 4 − v /2 ) 2 + ( v 3 ​ /2 ) 2 = 16 − 4 v + v 2 . Minimum at d / d v = 0 ⇒ v = 2 m/s.

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