7-20 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} \vec r_1&=2.70\i-2.90\j+5.50\k\ut{m}\\ \vec r_2&=-2.10\i+3.30\j+5.40\k\ut{m}\\ m&=2.90\ut{kg}\\ \vec F&=3.00\i+7.00\j+5.30\k\ut{N}\\ t&=3.00\ut{s} \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} W&=\vec F\cdot \vec S\\ &=\vec F\cdot (\vec r_2-\vec r_1)\\ &=(3\i+7\j+5.3\k)\cdot(-4.8\i+6.2\j-0.1\k)\\ &=3\cdot(-4.8)+7\cdot6.2+5.3\cdot(-0.1)\\ &=28.47\ut{J}\\ &\approx 28.5\ut{J}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} P&=\frac{W}{t}\\ &=\frac{28.47\ut{J}}{3.00\ut{s}}\\ &=9.49\ut{W} \end{aligned} $$ $$\ab{c}$$ $$ \begin{aligned} \theta &=\cos^{-1}\frac{\vec r_1 \cdot \vec r_2}{r_1 r_2}\\ &=\cos^{-1}\frac{2.7\cdot(-2.1)+(-2.9\cdot3.3)+(5.5\cdot5.4)}{\sqrt{2.7^2+(-2.9)^2+5.5^2}\sqrt{(-2.1)^2+7^2+5.3^2}}\\ &=\cos^{-1}\(241 \sqrt{\frac{2}{1134965}}\)\\ &\approx 1.2451517333655098\ut{rad}\\ &\approx 1.25\ut{rad} \end{aligned} $$