Velocity of Wind: Calculate Direction & Speed

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To determine the wind direction and velocity affecting an airplane flying west at 255 km/h with a resultant velocity of 225 km/h directed South 70 degrees West, vector subtraction is necessary. The wind's velocity can be calculated by rearranging the equation R = v + V, where R is the resultant vector and V is the airplane's velocity. By subtracting the airplane's velocity vector from the resultant vector, the wind's velocity vector can be isolated. This involves adding the negative of the airplane's velocity vector to the resultant vector. The solution requires careful vector analysis to accurately find the wind's direction and speed.
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The question said that the airplane turned west for 255km/h, and the resultant was 225km/h South 70 degrees West. I have to find the wind direction and velocity. How?
 
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lia said:
The question said that the airplane turned west for 255km/h, and the resultant was 225km/h South 70 degrees West. I have to find the wind direction and velocity. How?
If v is the velocity of the wind and V is the velocity of the airplane relative to the wind then the resultant R is

R = v + V

where everything in bold is a vector. To find v subract V from both sides of the equation and do the vector subtraction. That is equivalent to adding -V to R. -V is the same length as V but in the opposite direction.
 

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