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A vector → A has a magnitude of 54.0 m and points in a direction 20.0° above the negative x axis. A second vector, → B , has a magnitude of 74.0 m and points in a direction 45.0° above the negative x axis. Using the component method of vector addition, find the magnitude of the vector → C = → A + → B .

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carlos2112

Answer:

[tex]|C|=125.0408406m[/tex]

Step-by-step explanation:

For easy calculations let's use the supplementary angles:

[tex]180-20=160[/tex]

[tex]180-45=135[/tex]

[tex]A_x=54cos(160)=-50.74340152[/tex]

[tex]A_y=54sin(160)=18.46908774[/tex]

[tex]B_x=74cos(135)=-52.32590181[/tex]

[tex]B_y=74sin(135)=52.32590181[/tex]

Now lets calculate the magnitude of the vector C:

[tex]C=C_x+C_y[/tex]

where:

[tex]C_x=A_x+B_x=-103.0693033[/tex]

[tex]C_y=A_y+B_y=70.79498955[/tex]

Finally:

[tex]|C|=\sqrt{(C_x)^{2} +(C_y)^{2} } =125.0408406m[/tex]

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