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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??
one year ago

Answers : (1)

Arun
22987 Points
							
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)
one year ago
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