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Vietnam Contests
Vietnam National Olympiad
1965 Vietnam National Olympiad
1
1
Part of
1965 Vietnam National Olympiad
Problems
(1)
minimum distance of 2 ships, a navy one and an enemy one
Source: Vietnamese MO (VMO) 1965
8/22/2018
At a time
t
=
0
t = 0
t
=
0
, a navy ship is at a point
O
O
O
, while an enemy ship is at a point
A
A
A
cruising with speed
v
v
v
perpendicular to
O
A
=
a
OA = a
O
A
=
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
u
u
at a angle
0
<
ϕ
<
π
/
2
0 < \phi < \pi /2
0
<
ϕ
<
π
/2
to the line
O
A
OA
O
A
. 1) Let
ϕ
\phi
ϕ
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
ϕ
\phi
ϕ
to minimize the distance? What are directions of the two ships when their distance is minimum?
geometry
minimum