4-27 할리데이 10판 솔루션 일반물리학

$$\begin{cases} \vec v_0 &= (290.0\ut{km/h},-30.0\degree)\\ \Delta x &= 700\ut{m}\\ \vec a &= -g\j\\ g &\approx 9.80665\ut{m/s^2}\\ \end{cases}$$ $$\begin{aligned} \vec v_0 &= (290.0\ut{km/h},-30.0\degree)\\ &=(\frac{725}{9}\ut{m/s},-30.0\degree)\\ &=\frac{725}{6 \sqrt{3}}\i-\frac{725}{18}\j\\ \end{aligned}$$
(a) $t=?$ $$\begin{aligned} \Delta x &= v_x t,\\ t&=\frac{\Delta x}{v_x}\\ &=\frac{700}{\frac{725}{6 \sqrt{3}}}\ut{s}\\ &=\frac{168\sqrt{3}}{29}\ut{s}\\ &\approx 10.0339495059\ut{s}\\ &\approx 10.0\ut{s} \end{aligned}$$
(b) $h=?$ $$\begin{aligned} \Delta y &= v_{y0}t+\frac{1}{2}a_yt^2\\ -h &= \(-\frac{725}{18}\)\(\frac{168\sqrt{3}}{29}\)+\frac{1}{2}(-g)\(\frac{168\sqrt{3}}{29}\)^2\\ h &=\frac{700}{\sqrt{3}}+\frac{42336}{841}g\\ &\approx 897.812649075\ut{m}\\ &\approx 898\ut{m} \end{aligned}$$