Addition of vectors is done by adding the components of the vectors
The total speed of the fan is approximately 9.43 m/s,
Direction of total wind 58° counterclockwise from the positive x-axis
The reason the value is correct is as follows:
The given parameters are:
The direction at which the fan blowing at 5 m/s is blowing = Easterly
The direction in which the fan blowing 8 m/s is blowing = Northerly
The total speed of the van, |v| ≈ 9.43 m/s
Required:
To find the total wind speed of the fans
Solution:
Taken the easterly direction as the ith component, and the northerly direction as the jth component, the vector representing the speed of the fan is presented as follows
v = 5·i + 8·j
The magnitude of the total wind speed of the fan, |v| = √(5² + 8²) = √(89) ≈ 9.43
The total wind speed of the fan , |v| ≈ 9.43 m/s
The direction of the total speed with respect to the x-axis, θ, is given as follows;
θ = arctan(8/5) ≈ 58°
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