2-61 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} H&=60\ut{m}\\ t_1&=t_2-1.6\ut{s}\\ t_2&:\text{Land}\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$ \begin{aligned} S&=v_0t+\frac{1}{2}at^2,\\ -H&=(0)t_2+\frac{1}{2}(-g){t_2}^2\\ H&=\frac{1}{2}g{t_2}^2\\ 60&=\frac{1}{2}g{t_2}^2\\ \end{aligned} $$ $$ \begin{aligned} t_2&=2\sqrt\frac{30}{g}\\ \end{aligned} $$ $$ \begin{aligned} t_1&=t_2-1.6\ut{s}\\ &=2\sqrt\frac{30}{g}-1.6\ut{s} \end{aligned} $$ $$ \begin{aligned} -S_1&=v_0t+\frac{1}{2}at^2,\\ &=(0)t_1+\frac{1}{2}(-g){t_1}^2\\ S_1&=\frac{1}{2}g{t_1}^2\\ &=\frac{1}{2}g{\(2\sqrt\frac{30}{g}-1.6\)}^2\\ &=\frac{2}{25} \left(5 \sqrt{30}-4 \sqrt{g}\right)^2\\ &=\frac{1133633-500 \sqrt{2941995}}{15625}\ut{m}\\ &\approx 17.66532879663275\ut{m} \end{aligned} $$ $$ \begin{aligned} \Ans&=H-S_1\\ &=60-\frac{1133633-500 \sqrt{2941995}}{15625}\\ &=\frac{500 \sqrt{2941995}-196133}{15625}\ut{m}\\ &\approx 42.33467120336724\ut{m}\\ &\approx 42\ut{m}\\ \end{aligned} $$