4-48 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} p:\text{Plane in Wind}\\ w:\text{Wind}\\ q:\text{Plane on Land}\\ \end{cases} $$ $$ \begin{cases} v_p&=p=125\ut{mi/h}\\ v_w&=w=55.0\ut{mi/h}\\ \vec v_q&=\vec q=125\j\ut{mi/h}\\ \end{cases} $$ $$ \begin{aligned} \vec p&=\vec q-\vec w\\ \vec q&=\vec p+\vec w\\ 125\j&=\vec p+\vec w\\ \end{aligned} $$ $$ \begin{cases} p_x+w_x&=0\\ p_y+w_y&=125\\ {p_x}^2+{p_y}^2&=125\\ {w_x}^2+{w_y}^2&=55 \end{cases} $$ $$ \begin{cases} \vec p &=\pm\cfrac{11\sqrt{2379}}{10}\i+\cfrac{1129}{10}\j\\ \vec w &= \mp\cfrac{11\sqrt{2379}}{10}\i+\cfrac{121}{10}\j\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} \theta_w&=\tan^{-1}\frac{\cfrac{121}{10}}{\mp\cfrac{11\sqrt{2379}}{10}}\\ \end{aligned} $$ $$ \begin{cases} \theta_{w1}&=\pi-\tan^{-1}\cfrac{11}{\sqrt{2379}}\\ \theta_{w2}&=\tan^{-1}\cfrac{11}{\sqrt{2379}}\\ \end{cases} $$ $$ \begin{cases} \theta_{w1}&\approx 2.919778183092999\ut{rad}\\ \theta_{w2}&\approx 0.2218144704967944\ut{rad}\\ \end{cases} $$ $$ \begin{cases} \theta_{w1}&\approx 2.92\ut{rad}\\ \theta_{w2}&\approx 0.222\ut{rad}\\ \end{cases} $$ $$\ab{b}$$ $$ \begin{aligned} \theta_p&=\tan^{-1}\frac{\cfrac{1129}{10}}{\pm\cfrac{11\sqrt{2379}}{10}}\\ \end{aligned} $$ $$ \begin{cases} \theta_{p1}&=\tan^{-1}\cfrac{1129}{11 \sqrt{2379}}\\ \theta_{p2}&=\pi-\tan^{-1}\cfrac{1129}{11 \sqrt{2379}} \end{cases} $$ $$ \begin{cases} \theta_{p1}&\approx 1.127167385801308\ut{rad}\\ \theta_{p2}&\approx 2.014425267788485\ut{rad}\\ \end{cases} $$ $$ \begin{cases} \theta_{p1}&\approx 1.13\ut{rad}\\ \theta_{p2}&\approx 2.01\ut{rad}\\ \end{cases} $$