4-41 할리데이 11판 솔루션 일반물리학

$$\begin{cases} r_1 &=720\ut{m}\\ \theta_1&=40\degree\\ r_2&=1580\ut{m}\\ \Delta \theta&=123\degree \end{cases}$$ $$\begin{aligned} \theta_2&=40\degree+123\degree\\ &=163\degree \end{aligned}$$ $$\begin{cases} \vec r_1 &= 720\cos40\degree\i+ 720\sin40\degree\j\\ \vec r_2 &=1580\cos163\degree\i+1580\sin163\degree\j\\ \end{cases}$$ $$\begin{aligned} \Delta \vec r &=\vec r_2 - \vec r_1,\\ &=(-1580 \cos17\degree-720 \cos 40\degree)\i\\ &~~~~~~~+(1580 \sin17\degree-720 \sin 40\degree)\j \end{aligned}$$ $$\ab{a}$$ $$\begin{aligned} \Delta r &= 20 \sqrt{5688 \sin 33\degree+7537}\\ &\approx 2062.513692673625\ut{m}\\ &\approx 2.1\ut{km}\\ \end{aligned}$$ $$\ab{b}$$ $$\begin{aligned} \theta&=-\tan ^{-1}\left(\frac{79 \sin 17\degree-36 \sin 40\degree}{79 \cos 17\degree+36 \cos 40\degree}\right)-\pi\\ &\approx -3.141175790642246\ut{rad}\\ &\approx -3.1\ut{rad}\\ \end{aligned}$$