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airportsAandBaresuchthatAB=(600i+200j)km.anaircraftistobeflowndirectlyfromAtoB.theair...
airports A and B are such that AB=(600i+200j)km.an aircraft is to be flown directly from A to B.the aircraft can maintain a steady speed of 390km\h in still air. there is a wind blowing with velocity (30i-20j)km\h.find,in the form ai+bj,the velocity vector the pilot should set so that this velocity. together with the wind, causes the plane to travel directly from A to B
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(30i-20j)+(ai+bj)=(30+a)i+(b-20)j
(30+a)/(b-20)=600/200=3
a=3b-90
显然b-20>0,b>20
而a^2+b^2=390^2
(3b-90)^2+b^2=390^2
b^2-54b-96*150=0
(b-150)(b+96)=0
b=150或b=-96(舍弃)
所以:a=3*150-90=360
所以:ai+bj=360i+150j
(30+a)/(b-20)=600/200=3
a=3b-90
显然b-20>0,b>20
而a^2+b^2=390^2
(3b-90)^2+b^2=390^2
b^2-54b-96*150=0
(b-150)(b+96)=0
b=150或b=-96(舍弃)
所以:a=3*150-90=360
所以:ai+bj=360i+150j
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