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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.

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.

Grade:12th pass

2 Answers

Vikas TU
14149 Points
4 years ago
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.
Gkmeruva
13 Points
2 years ago
Vp/sin 45°=Vw/sin x
400/1/√2=200√2/sin x
Sin x*400=200√2*1/√2
Sin x=1/2
x=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/s
T=d/V=1000/546-399
T=1.83hr

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