Question

3. Two fans blow at 5 ms^-1 in a easterly direction and 8ms^-1 in a Northerly

Answer 1

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°

Learn more about addition of vectors here:

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