Two boys are standing at the ends A and B of a ground where AB = a. The boy at B starts running in a direction perpendicular to AB with velocity v1. The boy at A starts running simultaneously with velocity v and catches the other boy in a time t, where t is

Velocity of A relative to B is given byvA/B=vA→-vB→=v→-v1→.....(1)By taking x-components of equation (1), we get0=vsinθ-v1⇒sinθ=v1v......(2)By taking Y -components of equation (1), we getvy=vcosθ......(3)Time taken by boy at A to catch the boy at B is given byt= Relative displacement along Y - axis  Relative velocity along Y -axis  =avcosθ=av·1-sin2θ=av·1-v1v2[From equation (1)] =av·v2-v12v2=av2-v12=a2v2-v12