Two particles having position vectors   and  are moving with velocities  and . If they collide after 2 seconds, the value of ‘ ’ is

It is clear from figure that the displacement vector  between particles  and  is

     ….(i)

Now, as the particles are moving in same direction

 and  are , the relative velocity is given by

      …(ii)

Now, we know

Substituting the values of  and  from equation (i) and (ii) and , then on solving we get