솔루션피아

$$ \begin{cases} H&=40\ut{m}\\ \Delta x &=14\ut{m}\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$ \begin{aligned} S&=v_0t+\frac{1}{2}at^2,\\ -H&=(0)t+\frac{1}{2}(-g)t^2\\ H&=\frac{1}{2}gt^2\\ \end{aligned} $$ $$ \begin{aligned} t&=\sqrt{\frac{2H}{g}} \end{aligned} $$ $$ \begin{aligned} v&=\frac{S}{t}\\ &=\frac{S}{\sqrt{\frac{2H}{g}}}\\ &=S\sqrt{\frac{g}{2H}}\\ &=(14)\sqrt{\frac{g}{2(40)}}\\ &=\frac{7}..

$$ \begin{cases} d&=0.65\ut{m}\\ v_B&=\frac{1}{3}v_A\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$ \begin{aligned} 2aS&=v^2-{v_0}^2\\ 2(-g)(d)&={v_B}^2-{v_A}^2\\ 2(-g)(0.65)&=\(\frac{1}{3}v_A\)^2-{v_A}^2 \end{aligned} $$ $$ \begin{aligned} v_A&=\frac{3}{4} \sqrt{\frac{13g}{5}}\\ &=\frac{3 }{400}\sqrt{\frac{2549729}{10}}\ut{m/s}\\ &\approx 3.787113099050515\ut{m/s}\\ &\approx 3.8\ut{m/s}\\ \end{aligne..

$$ \begin{cases} t_1&=1977/01/26\\ t_2&=1983/09/18\\ S&=30600\ut{km} \end{cases} $$ $$ \begin{aligned} t_2-t_1&=2426\ut{day}\\ \end{aligned} $$ $$ \begin{aligned} \bar v&=\frac{S}{t}\\ &=\frac{30600\ut{km}}{2426\ut{day}}\\ &=\frac{30600\ut{km}}{2426\ut{day}}\cdot\frac{1000\ut{m}}{1\ut{km}}\cdot\frac{1\ut{day}}{24\ut{h}}\cdot\frac{1\ut{h}}{3600\ut{s}}\\ &=\frac{2125}{14556}\ut{m/s}\\ &\approx 0.1..

$$ \begin{cases} v&=360\ut{km/h}\\ S&=2.00\ut{km} \end{cases} $$ $$ \begin{aligned} 2aS&=v^2-{v_0}^2\\ 2a(2)&=(360)^2-{0}^2\\ \end{aligned} $$ $$ \begin{aligned} a&=32400\ut{km/h^2}\\ &=3.24\times10^4\ut{km/h^2}\\ \end{aligned} $$

$$ \begin{cases} a&=(5.0-1.2t)\ut{m/s^2}\\ v(0)&=2.7\ut{m/s}\\ x(0)&=7.3\ut{m}\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} \Delta v&=\int_0^t a\dd t\\ &=\int_0^t (5-1.2t)\dd t\\ &=5t-\frac{3}{5}t^2 \end{aligned} $$ $$ \begin{aligned} \therefore v&=v(0)+\Delta v\\ &=2.7+5t-\frac{3}{5}t^2\\ \end{aligned} $$ $$ \begin{aligned} a&=5-1.2t_1=0\\ t_1&=\frac{25}{6}\ut{s}\\ \end{aligned} $$ $$ \begin{..

$$ \begin{cases} H&=60\ut{m}\\ t_1&=t_2-1.6\ut{s}\\ t_2&:\text{Land}\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$ \begin{aligned} S&=v_0t+\frac{1}{2}at^2,\\ -H&=(0)t_2+\frac{1}{2}(-g){t_2}^2\\ H&=\frac{1}{2}g{t_2}^2\\ 60&=\frac{1}{2}g{t_2}^2\\ \end{aligned} $$ $$ \begin{aligned} t_2&=2\sqrt\frac{30}{g}\\ \end{aligned} $$ $$ \begin{aligned} t_1&=t_2-1.6\ut{s}\\ &=2\sqrt\frac{30}{g}-1.6\ut{s} \end{ali..

$$ \begin{cases} v_A&=15\ut{km/h}\\ v_B&=30\ut{km/h}\\ \end{cases} $$ $$ \begin{aligned} \bar v&=\frac{S_A+S_B}{t_A+t_B}\\ &=\frac{2S}{\cfrac{S}{v_A}+\cfrac{S}{v_B}}\\ &=\frac{2}{\cfrac{1}{v_A}+\cfrac{1}{v_B}}\\ &=\frac{2}{\cfrac{1}{15}+\cfrac{1}{30}}\ut{km/h}\\ &=20\ut{km/h} \end{aligned} $$

$$ \begin{cases} t&=4.8\ut{s}\\ v_0&=0\\ v_1&=60\ut{km/h}=\frac{50}{3}\ut{m/s}\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} v&=v_0+at,\\ \frac{50}{3}&=0+a(4.8)\\ \end{aligned} $$ $$ \begin{aligned} a&=\frac{125}{36}\ut{m/s^2}\\ &\approx 3.472222222222222\ut{m/s^2}\\ &\approx 3.5\ut{m/s^2}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} S&=\frac{1}{2}(v+v_0)t,\\ &=\frac{1}{2}\(\frac{50}{3}+0\)..

$$ \begin{cases} t_0&:\text{Start}\\ t_1&:\text{Max Speed}\\ t_2&:\text{Stop}\\ t_A&:t_{0\rarr1}\\ t_B&:t_{1\rarr2}\\ \end{cases} $$ $$ \begin{cases} S_A&=2.1\ut{m}\\ v_1&=6.0\ut{m/s}\\ a_B&=-3.0\ut{m/s^2}\\ \end{cases} $$ $$\title{Time A}$$ $$ $$ $$ \begin{aligned} S&=\frac{1}{2}(v+v_0)t,\\ S_A&=\frac{1}{2}(v_1+v_0)t_A\\ 2.1&=\frac{1}{2}(6+0)t_A\\ \end{aligned} $$ $$ \begin{aligned} t_A&=\frac{..

$$ \begin{cases} S&=1.20\ut{m}\\ v_1&=530\ut{m/s}\\ \end{cases} $$ $$ \begin{aligned} S&=\frac{1}{2}(v+v_0)t,\\ 1.2&=\frac{1}{2}(530+0)t\\ \end{aligned} $$ $$ \begin{aligned} t&=\frac{6}{1325}\ut{s}\\ &\approx 0.004528301886792453\ut{s}\\ &\approx 4.54\times10^{-3}\ut{s}\\ &\approx 4.54\ut{ms}\\ \end{aligned} $$