6-23 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} m&=630\ut{kg}\\ S&=90.0\ut{m}\\ \theta&=10.2\degree\\ f_1&=62.0\ut{N}\\ v_0&=6.20\ut{m/s}\\ f_2&=50.0\ut{N}\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$\Sigma \vec F = m\vec a,$$ $$ \begin{aligned} m a&=mg\sin\theta-f \\ a&=g\sin\theta-\frac{f}{m} \end{aligned} $$ $$S=v_0t+\frac{1}{2}at^2,$$ $$\ab{a}$$ $$ \begin{aligned} t_1&=\frac{m v_0-\sqrt{2 m^2g S \sin\theta+m^2 {v_0}^2-2 mf_1 S}}{f_1-mg \sin\theta}\\ &\approx 7.359879829019155\ut{s}\\ &\approx 7.36\ut{s}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} t_2&=\frac{m v_0-\sqrt{2 m^2g S \sin\theta+m^2 {v_0}^2-2 mf_2 S}}{f_2-mg \sin\theta}\\ &\approx 7.331802737114836\ut{s}\\ &\approx 7.33\ut{s}\\ \end{aligned} $$