3-25 할리데이 10판 솔루션 일반물리학

$$\begin{cases} \vec p_1:(25,-90^\circ-30^\circ)\\ \vec p_2=30\hat j\\ \end{cases} $$ $$ \begin{aligned} \vec p_1 =& \bra{25\cos\(-120^\circ\)}\hat i+\bra{25\sin\(-120^\circ\)}\hat j\\ =&\(-\frac{25}{2}\)\hat i + \(-\frac{25}{2}\sqrt3\)\hat j \end{aligned} $$ $$\Sigma \vec p = \(-\frac{25}{2}\)\hat i + \(30-\frac{25}{2}\sqrt3\)\hat j$$ $$ \begin{aligned} \theta_{\Sigma\vec p}=&\tan^{-1}\(\frac{30-\frac{25}{2}\sqrt3}{-\frac{25}{2}}\)\\ =&\pi +\tan ^{-1}\left(\sqrt3-\frac{12}{5} \right)\\ =&2.6\ut{rad}\\ \end{aligned} $$