Question

Point A moves uniformly with velocity v so that the vector v so that the vector v is continually "aimed" at B which in its turn moves rectilinearly and
uniformly with velocity u < v . At the initial moment v perpendicular u and the points are separated by a distance l.How soon will the points converge ?

Answer 1

   A moves with a speed equal to v aiming towards B.  B moves vertically upwards (direction y) with a uniform speed u.

   Take the frame of reference of B.  B is stationary.  Since A is always approaching and is directed towards B, in this frame of reference, A is traveling along a straight line (along x axis).  So A does not move in y-direction.    This means that, the velocity of A in direction y is also equal to u in the inertial frame of reference.

  velocity of A in y direction = v_y = u
   velocity of A in x direction = v_x = ?

  Magnitude of speed ( velocity) of A =  √(v_x² + v_y²) = v  (given)

         Hence v_x = √(v² - u²)

  Let A meet

     The distance between them is L initially. 
     Time taken for A to meet B =  T = L / v_x  = L / √(v² - u²)

   Since the horizontal and vertical velocities of A are constant, A is moving in a straight line.  A travels a distance of :

       v * T = L * v /√(v² - u²)