2-12 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} a&=-g=-9.80665\ut{m/s^2}\\ h&=15\ut{m}\\ v_0&=-10\ut{m/s}\\ \end{cases} $$ $$\ab{a}$$ $$2aS=v^2-v_0^2,$$ $$ \begin{aligned} v&=\sqrt{2as+v_0^2}\\ &=\sqrt{2(-g)(-15)+(-10)^2}\\ &=\sqrt{100+30g}\\ &=\frac{1}{20}\sqrt{\frac{788399}{5}}\ut{m/s}\\ &\approx19.85445793770256\ut{m/s}\\ &\approx19.9\ut{m/s}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} S&=v_0t+\frac{1}{2}at^2\\ -15&=-10t-\frac{1}{2}gt^2\\ \end{aligned} $$ $$ \begin{aligned} t&=\frac{\sqrt{30 g+100}-10}{g}\\ &=\frac{200 \left(\sqrt{3941995}-1000\right)}{196133}\ut{s}\\ &\approx1.004875052918433\ut{s}\\ &\approx1.00\ut{s} \end{aligned} $$ $$ \begin{cases} a&=-g=-9.80665\ut{m/s^2}\\ h&=15\ut{m}\\ v_0&=10\ut{m/s}\\ \end{cases} $$ $$\ab{c}$$ $$2aS=v^2-v_0^2,$$ $$ \begin{aligned} v&=\sqrt{2as+v_0^2}\\ &=\sqrt{2(-g)(-15)+(10)^2}\\ &=\sqrt{100+30g}\\ &=\frac{1}{20}\sqrt{\frac{788399}{5}}\ut{m/s}\\ &\approx19.85445793770256\ut{m/s}\\ &\approx19.9\ut{m/s}\\ \end{aligned} $$ $$\ab{d}$$ $$ \begin{aligned} S&=v_0t+\frac{1}{2}at^2\\ -15&=10t-\frac{1}{2}gt^2\\ \end{aligned} $$ $$ \begin{aligned} t&=\frac{\sqrt{30g+100}+10}{g}\\ &=\frac{200 \left(1000+\sqrt{3941995}\right)}{196133}\ut{s}\\ &\approx3.04430747887429\ut{s}\\ &\approx3.04\ut{s} \end{aligned} $$