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Question

An aircraft flies at 400 km/h in still air. A wind of 2002 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 time of his journey if AB=1000 km.

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Solution

Let the time taken by the aircraft to reach point B be t
From figure AM=ABcos45o=1000×12=5002 m
Also AP=ABsin45o=1000×12=5002 m

S-N direction : AM=[Vw+Vswsin(45α)]t
5002=[Vw+Vswsin(45α)]t .............(1)

W-E direction : AP=[Vswcos(45α)]t
5002=[Vswcos(45α)]t .............(2)

Equating (1) & (2), Vswcos(45α)=Vswsin(45α)+Vw
400[cos(45α)sin(45α)]=2002

OR 12cos(45α)12sin(45α)=12

OR sin(45)cos(45α)cos(45)sin(45α)=12

sin(α)=12 α=30o

From (2), 5002=400cos(15)t
5002=400×0.966×t t=1.83 hr

517453_251724_ans.png

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