MathDB

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?

Problem Statement