Question

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 .

Answer 1

`|C|=125.0408406m`

Explanation:

For easy calculations let's use the supplementary angles:

`180-20=160`

`180-45=135`

`A_x=54cos(160)=-50.74340152`

`A_y=54sin(160)=18.46908774`

`B_x=74cos(135)=-52.32590181`

`B_y=74sin(135)=52.32590181`

Now lets calculate the magnitude of the vector C:

`C=C_x+C_y`

where:

`C_x=A_x+B_x=-103.0693033`

`C_y=A_y+B_y=70.79498955`

Finally:

`|C|=\sqrt{(C_x)^(2) +(C_y)^(2) } =125.0408406m`