VMO 1965 Problem 1

At a time $t = 0$ , a navy ship is at a point $O$ , while an enemy ship is at a point $A$ cruising with speed $v$ perpendicular to $OA = a$ . The speed and direction of the enemy ship do not change. The strategy of the navy ship is to travel with constant speed $u$ at a angle $0 < \phi < \pi /2$ to the line $OA$ .

1. Let $\phi$ be chosen. What is the minimum distance between the two ships? Under what conditions will the distance vanish?
2. If the distance does not vanish, what is the choice of $\phi$ to minimize the distance? What are directions of the two ships when their distance is minimum?