2-45 할리데이 10판 솔루션 일반물리학

$$\begin{cases} x_0 = H\\ x_1 =\frac{9}{25}H\\ x_2 = 0\\ t_{1\to2} = 1\ut{s}\\ v_0 = 0\\ a = -g = -9.80665\ut{m/s^2}\\ \end{cases}$$ $$H=?$$ $$\begin{cases} \Delta x = v_0t+\frac{1}{2}at^2\\ 2a\Delta x = v^2-v_0^2\\ \end{cases}$$ $$\begin{aligned} x_2-x_1 &= v_1t_{1\to2}+\frac{1}{2}(-g)t_{1\to2}^2 \\ 0-\frac{9}{25}H &= v_1(1)+\frac{1}{2}(-g)(1)^2 \\ \frac{9}{25}H &= \frac{1}{2}g-v_1 \taag{2-45-1}\\ \end{aligned}$$ $$\begin{aligned} 2(-g)(x_1-x_0) &= v_1^2-v_0^2\\ -2g\(\frac{9}{25}H-H\) &= v_1^2-0^2\\ \frac{32}{25}gH &= v_1^2\taag{2-45-2}\\ \end{aligned}$$ $$\title{Make System of Equations}$$ $$\begin{cases} \frac{9}{25}H &= \frac{1}{2}g-v_1 \\ \frac{32}{25}gH &= v_1^2\\ \end{cases}$$ $$\begin{aligned} H &= \frac{25}{2}g (\because -g<0, v_1<0)\\ &= \frac{25}{2}\cdot9.80665\ut{m/s^2} \\ &= \frac{196113}{1600}\ut{m/s^2} \\ &\approx122.583125\ut{m/s^2}\\ &\approx100\ut{m/s^2}\\ \end{aligned}$$