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Find the magnitude of the sumof these two vectors:5.60 m A,30.0°B 6.00 mmagnitude (m)

Find the magnitude of the sumof these two vectors:5.60 m A,30.0°B 6.00 mmagnitude-example-1
User OJ Kwon
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1 Answer

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In order to find the magnitude of the vectors given, let's find first the components

The component in the x-axis


C_X=5\cos (0)+6\cos (180+30)
C_X=-0.196

then the component in the y-axis


C_Y=5\sin (0)+6\sin (180+30)=-3

Then the magnitude can be calculated with the next formula


|M|=\sqrt[]{Cx^2+C_Y^2}

we substitute the values


|M|=\sqrt[]{(-0.196)^2+(-3)^2}=3.01m

The magnitude is 3.01m

then for the direction, we can use the next formula


\theta=\tan ^(-1)((C_Y)/(C_x))

we substitute the values


\theta=\tan ^(-1)((-3)/(-0.196))=86.26\text{\degree}

then because both components are negative the direction will be


\text{direction}=86.26+180=266.26\text{\degree}

User Vero
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