5-35 할리데이 11판 솔루션 일반물리학

$$\begin{cases} m&=4.00\ut{kg}\\ \vec F_1 &= 18.0\i\ut{N}\\ a&=14.0\ut{m/s^2},\theta_a=20.0\degree\\ \end{cases}$$ $$\ab{a}$$ $$\Sigma \vec F = m\vec a,$$ $$\begin{cases} \vec F_1 +\vec F_2&= m \vec a\\ \vec F_2&= m \vec a-\vec F_1\\ &=4(14\cos20\degree\i+14\sin20\degree)-18\i\\ &=(56\cos20\degree-18)\i+56\sin20\degree\j\ut{N}\\ &\approx 34.6\i+19.2\j\ut{N} \end{cases}$$ $$\ab{b}$$ $$\begin{aligned} F_2 &=\sqrt{\((56\cos20\degree-18\)^2+\(56\sin20\degree\)^2}\\ &=2 \sqrt{865-504\cos20\degree}\ut{N}\\ &\approx 39.56740674463779\ut{N}\\ &\approx 39.6\ut{N}\\ \end{aligned}$$ $$\ab{c}$$ $$\begin{aligned} \theta&=\tan^{-1}\frac{56\sin20\degree}{56\cos20\degree-18}\\ &\approx 0.5052923343710929\ut{rad}\\ &\approx 0.505\ut{rad}\\ \end{aligned}$$