4-15 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} \Delta x_1&=8.09\ut{m}\\ g_1&=9.8128\ut{m/s^2}\\ g_2&=9.7999\ut{m/s^2}\\ \end{cases} $$ $$S=v_0t+\frac{1}{2}at^2,$$ $$ \begin{aligned} 0&=(v_0\sin\theta)t+\frac{1}{2}(-g)t^2\\ 0&=v_0\sin\theta-\frac{1}{2}gt\\ \end{aligned} $$ $$\therefore t=\frac{2v_0}{g}\sin\theta$$ $$\Delta x = v_x t,$$ $$ \begin{aligned} \Delta x&= v_0\cos\theta \cdot \(\frac{2v_0}{g}\sin\theta\)\\ &=\frac{{v_0}^2}{g}\sin(2\theta) \end{aligned} $$ $$ \begin{cases} \Delta x_2&=\cfrac{{v_0}^2}{g_2}\sin(2\theta)\\ \Delta x_1&=\cfrac{{v_0}^2}{g_1}\sin(2\theta)\\ \end{cases} $$ $$ \begin{aligned} \frac{\Delta x_2}{\Delta x_1}&=\frac{g_1}{g_2}\\ \Delta x_2&=\frac{g_1}{g_2}\Delta x_1\\ \end{aligned} $$ $$ \begin{aligned} \Ans&=\Delta x_2-\Delta x_1\\ &=\(\frac{g_1}{g_2}-1\)\Delta x_1\\ &=\(\frac{9.8128}{9.7999}-1\)\cdot8.09\ut{m}\\ &=+\frac{104361}{9799900}\ut{m}\\ &\approx +0.01064919029786018\ut{m}\\ &\approx +1.06\ut{cm}\\ \end{aligned} $$