Figure shows an typical instantaneous state of the two particles during their motion as particle B is continuously aimed towards particle A. Let x be the horizontal distance between the two particles and y be the vertical distance between the two particles. From figure 2 we can write the motion of the particle B given by the following equations,
Now, integrating both side of (1a) from the t=0 to the time when A and B meet we obtain,
In the figure, we resolve all velocities along and perpendicular to the line connecting the two bodies.
If r is the distance between the two bodies then, as seen from the figure r decreases as at any given instant of time. Thus,
The same result can of course also be derived by transforming (1a,1b) to polar coordinates. Now if r is the vector connecting particles A and B then,
Using (4) can rewrite (1a,1b) as,
Integrating both side of (3), it would mean that,
Now we can use (2) to solve for from (5) as,