Addition of **vectors **is done by adding the **components **of the vectors

The **total **speed of the fan is approximately <u>9.43 m/s</u>,

Direction of total wind 58° counterclockwise from the positive x-axis

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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**| ≈ <u>9.43 m/s</u>

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**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**| ≈ **<u>9.43 m/s</u>**

The direction of the total speed with respect to the x-axis, θ, is given as follows;

θ = arctan(8/5) ≈ **<u>58°</u>**

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Learn more about **addition of vectors** here:

brainly.com/question/17691926