5-44 할리데이 11판 솔루션 일반물리학

$$\begin{cases} m&=0.600\ut{kg}\\ x(t\ut{s})&=-15.00+3.00t-2.00t^3\ut{m}\\ y(t\ut{s})&=25.00+7.00t-7.00t^2\ut{m}\\ t&=1.20\ut{s}\\ \end{cases}$$ $$\vec r=(-15+3t-2t^3)\i+(25+7t-7t^2)\j,$$\\ $$\begin{aligned} \vec v&=\dxt{\vec r}\\ &=\dt\bra{(-15+3t-2t^3)\i+(25+7t-7t^2)\j}\\ &=(3-6t^2)\i+(7-14t)\j\ut{m/s} \end{aligned}$$ $$\begin{aligned} \vec a&=\dxt{\vec v}\\ &=\dt\bra{(3-6t^2)\i+(7-14t)\j}\\ &=-12t\i-14\j\ut{m/s^2} \end{aligned}$$ $$\begin{aligned} \Sigma \vec F&=m\vec a\\ &=-7.2t\i-8.4\j\ut{N}\\ \end{aligned}$$ $$\ab{a}$$ $$\begin{aligned} \abs{\vec F}&=\sqrt{(7.2t)^2+8.4^2}\\ &=\frac{6}{5} \sqrt{36 t^2+49}\\ \end{aligned}$$ $$\begin{aligned} F(1.2)&=\frac{6 \sqrt{2521}}{25}\ut{N}\\ &\approx 12.050294602207863\ut{N}\\ &\approx 12.1\ut{N}\\ \end{aligned}$$ $$\ab{b}$$ $$\begin{aligned} \theta_{\vec F}&=\tan^{-1}\frac{-8.4}{-7.2t}\\ &=\tan ^{-1}\frac{-7}{-6t} \end{aligned}$$ $$\begin{aligned} \theta(1.2)&=\tan ^{-1}\frac{35}{36}-\pi\\ &\approx -2.3702780660152047\ut{rad}\\ &\approx -2.37\ut{rad}\\ \end{aligned}$$ $$\ab{c}$$ $$\begin{aligned} \vec v&=(3-6t^2)\i+(7-14t)\j\ut{m/s}\\ \theta_{v}&=\tan^{-1}\frac{7-14t}{3-6t^2}\\ &=\tan ^{-1}\frac{245}{141}-\pi\\ &\approx -2.093013953979933\ut{rad}\\ &\approx -2.09\ut{rad}\\ \end{aligned}$$