steamboat
For point C, when the ship sails from west to east, the ship is closest to the typhoon center.
distance
It is the length of AC.
When the typhoon center moves to A, the time taken is
100 ÷ 40 = 2.5h At this time, the shortest distance between the ship and the typhoon center AC = 20× 2.5 = 50 < 20 √ 10.
therefore
Ships will encounter typhoons.
Suppose the first time a ship encounters a typhoon is t, the ship sails to C, and the typhoon travels to E on the AB line. Then AC=20t, BE=40t, CE=20√ 10.
From the Pythagorean theorem, it is concluded that
(20t)^+( 100-40t)^=(20√ 10)^
therefore
t= 1
or
t=3
because
When t=3, 40t = 120 > 100, which is inconsistent.
Title meaning
Give it up.
therefore
When the ship encounters a typhoon for the first time, when the ship sails 1 hour.
(2) The crossing point D is north of DF⊥.
direction indicator
, then
AF= 1/2
AD= 1/2
×60=30 nautical miles, DF=30√3 nautical miles.
because
Ad = 60 < 20 √ 10, so
When the typhoon reaches A, D is affected by the typhoon.
Suppose that the place where D was first affected by the typhoon was G, that is,
DG=20√ 10
therefore
fg^=dg^-df^=(20√ 10)^-(30√3)^= 1300
therefore
FG = 10√ 13≈ 10×3.6 = 36
rule
BG=BF-FG= 100+30-36=94
therefore
The time for the typhoon to reach G is 94÷40=2.35.
time
therefore
Ship speed: 60÷2.35≈26 knots.