Let
be the distance from the origin to the particle
and let
be the distance from the origin to the particle
. Also Let
be the distance between
and
. Notice that
and
are functions of time and we shall thus write them as
respectively.
By the given information, we have
units/min and
units/min. Using the initial positions, then we see that
and
. We can relate these two functions by Pythagoras' theorem: we have
, and therefore
Now, we will first determine the time
at which the distance between the particles is
units. We do this by setting
and solving for
. This gives
and therefore
(we can ignore the negative root since time cannot be negative).
Next, we want to find
when
. By differentiating both sides of the equation
, we get
. Now we can plug in
and
, which gives
.