题目内容
甲船在岛B的正南A处,AB=10 n mile,甲船自A处以4 n mile/h的速度向正北航行,同时乙船以6 n mile/h的速度自岛B出发,向北偏东60°方向驶去,则两船相距最近时经过了________ min.
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设甲、乙两船行驶x h后,分别位于C,D,
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CD=y,如图所示.
在△CBD中,
y2=(10-4x)2+(6x)2-2(10-4x)·6x·cos120°=28x2-20x+100=28(x-
)2+
,
所以当x=
h,即x=
×60=
min时,
=
.
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CD=y,如图所示.
在△CBD中,
y2=(10-4x)2+(6x)2-2(10-4x)·6x·cos120°=28x2-20x+100=28(x-
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所以当x=
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