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a person traveling eastward with a speed of 3 km/h finds that wind seems to blow from north.on doubling his speed the wind appears to flow from northeast.find the magnitude of the actual velocity of the wind??

a person traveling eastward with a speed of 3 km/h finds that wind seems to blow from north.on doubling his speed the wind appears to flow from northeast.find the magnitude of the actual velocity of the wind??

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1 Answers

Arun
25750 Points
5 years ago
Using +x = east and +y = north 

Suppose velocity of wind is (X, Y) 

Velocity of person, V = (3, 0) 
Velocity of wind relative to person = (X,Y) - (3, 0) = (X – 3, Y) 
Since wind appears to blow directly from the north, the east-west component (X – 3) must be zero: 
X -3 = 0 
X = 3km/hr 

Velocity of person, V = (6, 0) 
Velocity of wind relative to person = (X,Y) - (6, 0) = (X-6, Y) = (3- 6, Y) = (- 3, Y) 
Since relative velocity is from the north east (direction south west), this is an angle of tan-1(1) = 45degrees.(south of west). 
The x and y components of the relative velocity must be equal, beecause tan(45)=1, so Y = -3km/hr 

Wind vector = (X, Y) = (3, -3) km/hr 
Wind velocity = sqrt(3^2 + 3^2) = 4.2km/hr 
Direction to the south east (from the north west)

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