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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 ?

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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 :