[Math] Determine the magnitude of the vector sum

physics

Determine the magnitude of the vector sum $V = V1 + V2$ and the angle $θx$ which $V$ makes with the positive x-axis.

problem1

I get $B$ to be 37.0414 but I am not sure what to add it do to get the correct angle.

Best Answer

Here's the easiest way: find the components of $V_1$ and $V_2$ explicitly to find $V$. Once you have the components of $V$, it is easy to get its magnitude and the angle it makes with the $x$-axis.

Let $\theta_1$ be the angle $V_1$ makes with the x axis and $\theta_2$ be the same for $V_2$.

To start, we have $$ \tan\theta_1=3/6=\frac12 $$ From there, do some quick manipulation to find $\sin\theta_1$ and $\cos\theta_1$. We have $$ V_1=(9\cos\theta_1,9\sin\theta_1)=(8.05,4.02) $$ Now, $V_2$ makes an angle of $180˚-63˚=117˚=\theta_2$ with the x-axis. So, we have $$ V_2=(12\cos\theta_2,12\sin\theta_2)=(-5.45,10.69) $$ From there, we have $$ V=V_1+V_2=(2.60,14.71) $$ Now, it's simply a matter of finding $$ |V|=\sqrt{2.60^2+14.71^2}=14.9\\ \theta_x=\arctan(14.71/2.6)=80˚ $$

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