# 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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by Souvik118
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2014-12-21T01:27:42+05:30

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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 :

v * T = L * v /√(v² - u²)

u r welcome