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An aircraft flies at 400 km/h in still air . A wind of 200√2 km/h is blowing from the south . The pilot wishes to travel from A to a point B north east of A . Find the direction he must steer and the time of his journey if AB = 1000 km.
we know the resulatnt. that is north east of A.Therefore,let v km / h be the change in velocity of aircraft.then,perpendiclar / hypertenuse = sin45.200root2/root((400+v)^2 + (200root2)^2) = sin45.Solve here for v.
Vp/sin 45°=Vw/sin x400/1/√2=200√2/sin xSin x*400=200√2*1/√2Sin x=1/2x=30°Time =distance/velocity=Vpg=√Vp^2+Vw^2+2*Vp*Vw*cos(45+x)Vpg=√400^2+200√2^2+2*400*200√2cos75°Vpg=√200(800)+400+800√2*0.2588=546.399m/sT=d/V=1000/546-399T=1.83hr
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