Finding distance between two points A, B moving in a plane

[Richlair]

A and B are two objects in a plane. Initially they were at a distance d apart. B moves rectilinearly and perpendicular to the line AB initially with speed v and A moves with speed v so that it is continually aimed towards B. After some time, both of them are moving aimed in the same direction and would be a fixed distance apart. Find the fixed distance.

 

[vkash]

A and B are two objects in a plane. Initially they were at a distance d apart. B moves rectilinearly and perpendicular to the line AB initially with speed v and A moves with speed v so that it is continually aimed towards B. After some time, both of them are moving aimed in the same direction and would be a fixed distance apart. Find the fixed distance.

I assume that their speed |velocity| is same[/color]
First consider first particle A is at 0i+0j and second particle B is at di+0j here i and j represent unit vectors along x and y direction. now B start moving with velocity Vb=0i+vj it's location at time t is Rb=(0i+vj)t+di. Now come to first particle A. let it's velocity at any time is vx i+vy j. since velocity of both A and B is same so (vx²+vy²))^1/2=v. one more constraint is it's direction is always along the location of B that is (0i+vj)t+di now using all the constraint i mentioned you can do this question.
Hope now you will complete it.

 

[Fewmet]

I assume that their speed |velocity| is same[/color]
First consider first particle A is at 0i+0j and second particle B is at di+0j here i and j represent unit vectors along x and y direction. now B start moving with velocity Vb=0i+vj it's location at time t is Rb=(0i+vj)t+di. Now come to first particle A. let it's velocity at any time is vx i+vy j. since velocity of both A and B is same so (vx²+vy²))^1/2=v. one more constraint is it's direction is always along the location of B that is (0i+vj)t+di now using all the constraint i mentioned you can do this question.
Hope now you will complete it.

I was thinking much the same, but I would solve it in B's frame of reference. That mean treating B as at rest and A with initial leftward velocity of v and initial downward velocity (assuming B was moving upwards) of -v.

 

[Richlair]

I assume that their speed |velocity| is same[/color]
First consider first particle A is at 0i+0j and second particle B is at di+0j here i and j represent unit vectors along x and y direction. now B start moving with velocity Vb=0i+vj it's location at time t is Rb=(0i+vj)t+di. Now come to first particle A. let it's velocity at any time is vx i+vy j. since velocity of both A and B is same so (vx²+vy²))^1/2=v. one more constraint is it's direction is always along the location of B that is (0i+vj)t+di now using all the constraint i mentioned you can do this question.
Hope now you will complete it.

How should I use the constraint that A is headed towards B at any instant?