The Vector Jogger

Calculus Level 2

A jogger is jogging around a circular park of radius 1 kilometer at a speed of 6.28 kilometers per hour. The jogger starts at some point $A$ , and jogs around the park to a point $B$ , diametrically opposite to $A$ . During his jog, how many minutes after starting from $A$ , does the ratio between the jogger's distance and the jogger's displacement reach a maximum?

Details:

Take $\pi\approx 3.14$

The ratio to be maximized is $\frac{Distance}{Displacement}$