Question

The magnitudes of the vectors A=5m 90 degrees, B=18m C=21m 40 degrees. Find magnitude and direction

Answer 1

We will have the following:

Magnitude:

`x=\sqrt[]{(18.0+21.0\cdot\cos(40.0))^2+(-5.0+21.0\sin(40.0))^2}\Rightarrow x=35.13038857`
`\Rightarrow x\approx35.1`

So, its magnitude is approximately 35.1 meters.

Now, we calculate its direction:

`\tan (\theta)=(21\sin(40)-5)/(18+21\cos(40))\Rightarrow\theta=\arctan ((21\sin (40)-5)/(18+21\cos (40)))`
`\Rightarrow\theta=13.9995455\Rightarrow\theta\approx14.0`

So, the direction is approximately 14.0°.

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