4-4 할리데이 10판 솔루션 일반물리학

$$\begin{cases} t_0=15\ut{min}\\ t_1=30\ut{min}\\ t_2=t_1+30\ut{min}\\ t_3=t_2+60\ut{min}\\ \end{cases}$$
(a)(b)$\Delta \vec r_{0\to1}=?$ $$\begin{aligned} \Delta\vec r_{0\to1} =& \vec r_1-\vec r_0\\ =&(12,\pi)-(12,\frac{\pi}{2})\\ =&(-12\j)-(12\i)\\ =&-12\i-12\j\\ \end{aligned}$$
(a)$\abs{\Delta r_{0\to1}}=?$ $$\begin{aligned} \abs{\Delta r_{0\to1}}=&\sqrt{(-12)^2+(-12)^2}\\ =&12\sqrt2\\ \approx&17\ut{cm} \end{aligned}$$
(b)$\phi_{0\to1}=?$ $$\begin{aligned} \phi_{0\to1}=&\cos^{-1}\(\frac{\vec r_0 \cdot \vec r_1}{\abs{r_0}\abs{r_1}}\)\\ =&\frac{\pi}{2}\ut{rad} \end{aligned}$$
(c)(d)$\Delta \vec r_{1\to2}=?$ $$\begin{aligned} \Delta\vec r_{1\to2} =& \vec r_2-\vec r_1\\ =&(12,\frac{3}{2}\pi)-(12,\frac{\pi}{2})\\ =&(-12\i)-(12\i)\\ =&-24\i\\ \end{aligned}$$
(c)$\abs{\Delta r_{1\to2}}=?$ $$\abs{\Delta r_{1\to2}}=24$$
(d)$\phi_{1\to2}=?$ $$\phi_{1\to2}=\pi$$
(e)(f)$\Delta \vec r_{2\to3}=?$ $$\begin{aligned} \Delta\vec r_{2\to3} =& \vec r_3-\vec r_2\\ =&(12,\frac{3}{2}\pi+2\pi)-(12,\frac{3}{2}\pi)\\ =&(12,\frac{3}{2}\pi)-(12,\frac{3}{2}\pi)\\ =&0 \end{aligned}$$
(e)$\abs{\Delta r_{2\to3}}=?$ $$\abs{\Delta r_{2\to3}} = 0$$
(f)$\phi_{2\to3}=?$ $$\phi_{2\to3}=0$$