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Spain Contests
Spain Mathematical Olympiad
1971 Spain Mathematical Olympiad
6
6
Part of
1971 Spain Mathematical Olympiad
Problems
(1)
the fastest path a submarine to move
Source: Spanish Mathematical Olympiad 1971 P6
12/5/2022
The velocities of a submerged and surfaced submarine are, respectively,
v
v
v
and
k
v
kv
k
v
. It is situated at a point
P
P
P
at
30
30
30
miles from the center
O
O
O
of a circle of
60
60
60
mile radius. The surveillance of an enemy squadron forces him to navigate submerged while inside the circle. Discuss, according to the values of
k
k
k
, the fastest path to move to the opposite end of the diameter that passes through
P
P
P
. (Consider the case particular
k
=
5
k =\sqrt5
k
=
5
.)
algebra
inequalities