2-60 할리데이 10판 솔루션 일반물리학

$$ \begin{cases} t_1 = \text{Rock is Top of Building}\\ t_2 = \text{Rock is High Point}\\ \end{cases} $$ $$\begin{cases} t_1=1.5\ut{s}\\ t_2=2.5\ut{s}\\ x_0 = 0 \\ x_1 = h \\ v_0 > 0 \\ a=-g = -9.80665\ut{m/s^2}\\ \end{cases} $$ $$ h=?$$ $$ \Delta x = vt-\frac{1}{2}at^2,$$ $$ \begin{aligned} \Delta x_{0\to2} &= v_2t_{0\to2}-\frac{1}{2}(-g)t_{0\to2}^2\\ (x_2-x_0) &= v_2(t_2-t_0)+\frac{1}{2}gt(t_2-t_0)^2\\ x_2 &= \frac{1}{2}gt_2^2\taag{2-60-1}\\ \end{aligned} $$ $$ \begin{aligned} \Delta x_{1\to2} &= v_2t_{1\to2}-\frac{1}{2}(-g)t_{1\to2}^2\\ (x_2-x_1) &= v_2(t_2-t_1)+\frac{1}{2}gt(t_2-t_1)^2\\ x_2-h &= \frac{1}{2}g(t_2-t_1)^2\\ h &= x_2-\frac{1}{2}g(t_2-t_1)^2\\ &= \frac{1}{2}gt_2^2-\frac{1}{2}g(t_2-t_1)^2\reef{2-60-1}\\ &= \frac{1}{2} g t_1 \left(2 t_2-t_1\right)\\ &= \frac{1}{2} (9.80665\ut{m/s^2}) (1.5\ut{s}) \left\{2 (2.5\ut{s})-(1.5\ut{s})\right\}\\ &= \frac{4118793}{160000}\ut{m}\\ &=25.74245625\ut{m}\\ &\approx 26\ut{m}\\ \end{aligned} $$