4-23 할리데이 10판 솔루션 일반물리학

$$\begin{cases} \vec a &= -g\j\\ g &\approx 9.80665\ut{m/s^2}\\ \end{cases}$$ $$\begin{cases} h &= 40.4\ut{m}\\ \vec v_0 &= 285\i\ut{m/s}\\ \end{cases}$$
(a) $t=?$ $$\begin{aligned} \Delta y &= v_{y0}t+\frac{1}{2}a_yt^2,\\ -h &= (0)t+\frac{1}{2}(-g)t^2\\ h &= \frac{1}{2}gt^2\\ t &=\sqrt{\frac{2h}{g}}\\ &\approx2.8704193075\ut{s}\\ &\approx2.87\ut{s} \end{aligned}$$
(b) $\Delta x=?$ $$\begin{aligned} \Delta x &= v_x t\\ &=v_x \sqrt{\frac{2h}{g}}\\ &\approx 818.069502637\ut{m}\\ &\approx 818\ut{m}\\ \end{aligned}$$
(c) $v_{tx}=?$ $$\begin{aligned} v_{tx} &= v{x0} \\ &= 285\ut{m/s} \end{aligned}$$
(d) $v_{ty}=?$ $$\begin{aligned} 2a\Delta y &= v_y^2-v_{y0}^2,\\ 2(-g)(-h) &= v_y^2-(0)^2\\ v_y &= \sqrt{2gh}\\ &\approx 28.1491975019\ut{m}\\ &\approx 28.1\ut{m}\\ \end{aligned}$$