2-63 할리데이 10판 솔루션 일반물리학

$$\begin{cases} t_1 = \text{FlowerPot is Bottom of Window}\\ t_2 = \text{FlowerPot is Top of Window}\\ t_3 = \text{FlowerPot is Top Point}\\ \end{cases}$$ $$\begin{cases} x_0=0\\ x_{1\to2}=2.00\ut{m}\\ t_{1\to2}=0.50\ut{s}\\ v_3=0\\ a=-g = -9.80665\ut{m/s^2}\\ \end{cases}$$ $$x_{2\to3}=?$$ $$\Delta x = vt-\frac{1}{2}at^2,$$ $$\Delta x_{1\to2} = v_2t_{1\to2}-\frac{1}{2}(-g)t_{1\to2}^2$$ $$\begin{aligned} v_2&=\frac{\Delta x_{1\to2}}{t_{1\to2}}-\frac{t_{1\to2}g}{2}\\ &=\frac{2.00}{0.50}-\frac{0.50g}{2}\\ &=4-\frac{g}{4}\\ \end{aligned}$$ $$\begin{aligned} 2a\Delta x &= v^2-v_0^2,\\ 2(-g)\Delta x_{2\to3} &= v_3^2-v_2^2\\ -2g\Delta x_{2\to3} &= 0^2-v_2^2\\ \Delta x_{2\to3} &=\frac{v_2^2}{2g}\\ &=\frac{(4-\frac{g}{4})^2}{2g}\\ &=\frac{g}{32}+\frac{8}{g}-1\\ &=\frac{9.80665}{32}+\frac{8}{9.80665}-1\\ &=\frac{15343033689}{125525120000}\ut{m}\\ &= 0.122231\ut{m}\\ &\approx 12.2\ut{cm}\\ \end{aligned}$$