Q. 1.13 - "Problems in General Physics" by I.E. Irodov

Question: Point A moves uniformly with velocity v so that the vectoris continually ”aimed”at point B which in its turn moves rectilinearlyand uniformly with velocity u . At the initial moment of time⊥and the points are separated by a distance l. How soon will the pointsconverge?

Answer: Lets consider an arbitrary time when the point A is at a distance of x from point B.

Taking point B’s velocity component along the direction of A velocity, the two
points are coming closer at a speed given by

Integrating this equation,

where τis the required time. This gives:

Also, when the points meet, the two points must have traveled an equal
distance along the direction in which point B travels. Thus,

I.e. the two points will meet after a time given by .