Find the time an aeroplane having velocity v (relative to air), takes to fly around a square with side a and the wind blowing at a velocity u, in the two cases,
Text Solution
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Sol. Relative velocity along AB → u + v
BC → 
CD → v – u
DA → 
∴ time taken
t = 
+ 
+ 
+ 
= 
+ a 
= 
+ a 
= 
+ 
= 2a 
t = 2a 
t = 
Along AB
Let w 1 is the resultant velocity
w 1 = 
+ v cos θ
= 
+ v 
= 
+ v 
Similarly , we can show that
Along BC Resultant velocity
w 2 = v 
– 
Along CD Resultant velocity
w 3 = v 
– 
Along DA Resultant velocity
w 4 = 
+ v 
∴ Total time taken :-
t = 
+ 
+ 
+ 
= 
+ 
= 
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