4-9 할리데이 11판 솔루션 일반물리학

$$\begin{cases} v_a&=23.0\ut{m/s}\\ v_b&=33.6\ut{m/s}\\g&=9.80665\ut{m/s^2}\\ \end{cases}$$ $$\ab{a}$$ $$v_a = v_x,$$ $$\begin{aligned} \Delta x &= v_x t\\ &=v_a t\\ &=23\ut{m/s}\cdot5\ut{s}\\ &=115\ut{m} \end{aligned}$$ $$\ab{b}$$ $${v_x}^2+{v_y}^2=v^2,$$ $$\begin{aligned} 2aS&=v^2-{v_0}^2\\ 2(-g)(H)&=0^2-{v_{y0}}^2\\ 2gH&={v_{y0}}^2\\ \end{aligned}$$ $$\begin{aligned} H&=\frac{v^2-{v_x}^2}{2g}\\ &=\frac{33.6^2-23^2}{2g}\\ &=\frac{14999}{50g}\\ &=\frac{5999600}{196133}\ut{m}\\ &\approx 30.58944695691189\ut{m}\\ &\approx 30.6\ut{m}\\ \end{aligned}$$