4-35 할리데이 11판 솔루션 일반물리학

$$\begin{cases} H&=2.24\ut{m}\\ a&=9.0\ut{m}\\ x_0&=-7.0\ut{m}\\ y_0&=3.0\ut{m}\\ \vec v_0&=v_0\i \end{cases}$$ $$\ab{a}$$ $$\begin{aligned} S&=v_0t+\frac{1}{2}at^2,\\ \Delta y&=(0)t+\frac{1}{2}(-g)t^2\\ -3&=-\frac{1}{2}gt^2\\ t&=\sqrt{\frac{6}{g}}\\ \end{aligned}$$ $$\begin{aligned} \Delta x &= v_x t\\ 7 &= v_x \sqrt{\frac{6}{g}}\\ \end{aligned}$$ $$\begin{aligned} v_x &=7\sqrt{\frac{g}{6}}\\ &\approx 8.949169887015593\ut{m/s}\\ &\approx 8.9\ut{m/s}\\ \end{aligned}$$ $$\ab{b}$$ $$\begin{aligned} S&=v_0t+\frac{1}{2}at^2,\\ \Delta y&=(0)t+\frac{1}{2}(-g)t^2\\ -3-2.24&=-\frac{1}{2}gt^2\\ t&=\sqrt{\frac{262}{25g}}\\ \end{aligned}$$ $$\begin{aligned} \Delta x &= v_x t\\ 7+9 &= v_x \sqrt{\frac{262}{25g}}\\ \end{aligned}$$ $$\begin{aligned} v_x &=40\sqrt{\frac{2g}{131}}\\ &\approx 15.47745960179483\ut{m/s}\\ &\approx 15\ut{m/s}\\ \end{aligned}$$