7-32 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} \vec d_i&=3.00\i-2.00\j+5.00\k\ut{m}\\ \vec d_f&=-5.00\i+4.00\j+7.00\k\ut{m}\\ m&=2.00\ut{kg}\\ \vec F &= 4.50\i+8.50\j+6.00\k\ut{N}\\ t&= 4.00\ut{s} \end{cases} $$ $$ \begin{aligned} \vec S &= \vec d_f-\vec d_i\\ &=-8\i+6\j+2\k\ut{m} \end{aligned} $$ $$\ab{a}$$ $$W=\vec F \cdot \vec S,$$ $$ \begin{aligned} W&=4.5\cdot(-8)+8.5\cdot6+6\cdot2\\ &=27\ut{J}\\ &=27.0\ut{J}\\ \end{aligned} $$ $$\ab{b}$$ $$P=\dxt{W},$$ $$ \begin{aligned} P&=\frac{27}{4}\ut{W}\\ &=6.75\ut{W}\\ \end{aligned} $$ $$\ab{c}$$ $$ \begin{aligned} \theta&=\cos^{-1}\frac{\vec d_i\cdot\vec d_f}{d_id_f}\\ &=\cos^{-1}\frac{12}{\sqrt{38}\cdot3\sqrt{10}}\\ &=\cos^{-1}\frac{2}{\sqrt{95}}\\ &\approx 1.364132699103351\ut{rad}\\ &\approx 1.36\ut{rad}\\ \end{aligned} $$