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

Answer:

$|C|=125.0408406m$

Step-by-step 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:

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