4-68 할리데이 11판 솔루션 일반물리학

$$\begin{cases} \Delta t &= 3.15\ut{h}\\ \Delta \vec r &= 11.2\i+24.5\j+2.88\k\ut{km} \end{cases}$$ $$\ab{a}$$ $$\begin{aligned} \bar v &= \frac{\Delta r}{\Delta t}\\ &= \frac{\sqrt{11.2^2+24.5^2+2.88^2}}{3.15}\ut{km/h}\\ &=\frac{2\sqrt{1834961}}{315}\ut{km/h}\\ &\approx 8.600681416985678\ut{km/h}\\ &\approx 8.60\ut{km/h}\\ \end{aligned}$$ $$\ab{b}$$ $$\begin{aligned} \vec n &= 0\i+0j+1\k,\\ \frac{\pi}{2}-\theta&=\cos^{-1}\frac{\vec r\cdot\vec n}{r n}\\ &=\cos^{-1}\frac{2.88}{\sqrt{11.2^2+24.5^2+2.88^2}}\\ &=\cos^{-1}\frac{144}{\sqrt{1834961}}\\ \theta &= \frac{\pi}{2}-\cos^{-1}\frac{144}{\sqrt{1834961}}\\ &\approx 0.1065051091644924\ut{rad}\\ &\approx 0.107\ut{rad}\\ \end{aligned}$$