Runner sprints around a circular track of radius  m at a constant speed of          m/s.

Runners friend is standing at a distance of  m from the center of track.

Draw a rough diagram for the situation at any time .

Consider the  as the central angle at .

Therefore,

.

Length of the arc .

Differentiate on each side with respect to .

.

Substitute and  in above expression.

Apply cosine rule to the .

.

Differentiate on each side with respect to .

Distance between the two runners is  m.

Therefore, .

Substitute  in .

Now the value for .

Consider .

Substitute  ,  and in above expression.

Distance between the friends is changing at rate of m/s.

Distance between the friends is changing at rate of m/s.