Question

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

Answer 1

Let us locate the point A and B at an arbitrary instant of time (Fig.).

If A and B are separated by the distance s at this moment, then the points converge or point A approaches B with velocity  -ds/dt =v-u cosα where angle α varies with time.

As both A and B cover the same distance in x-direction during the sought time interval, so the other condition which is required can be obtained by the equation