솔루션피아

$$ \begin{cases} S &= 4350\ut{km}\\ t_W-t_E &= 70.0\ut{min}\\ v_{P\larr A} &=850\ut{km/h}\\ \vec v_A &= v_A\i \end{cases} $$ $$ \begin{cases} v_W &= v_{P\larr A}-v_A\\ v_E &= v_{P\larr A}+v_A \end{cases} $$ $$ \begin{cases} v_W &= \frac{S}{t_W}\\ v_E &= \frac{S}{t_E}\\ \end{cases} $$ $$ \begin{aligned} t_W-t_E &=\frac{S}{v_W}-\frac{S}{v_E}\\ \Delta t&=\frac{S}{v_{P\larr A}-v_A}-\frac{S}{v_{P\lar..

$$ \begin{cases} v_0&=40.0\ut{m/s}, \theta_0=30.0\degree\\ \Delta x &=150\ut{m}\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$ \begin{aligned} \Delta x&=v_x t,\\ 150&=40\cos30\degree t\\ t&=\frac{5\sqrt3}{2}\ut{s}\\ \end{aligned} $$ $$\ab{a}$$ $$ \begin{aligned} \Delta y&=v_0t+\frac{1}{2}at^2,\\ &=(40\sin30\degree)\(\frac{5\sqrt3}{2}\)+\frac{1}{2}(-g)\(\frac{5\sqrt3}{2}\)^2\\ &=50 \sqrt{3}-\frac{75 g}..

$$ \begin{cases} \vec r&=4.0t\i+4.0\sin\cfrac{\pi t}{4.0}\j \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} \vec r(t)&=4t\i+4\sin\frac{\pi t}{4}\j,\\ \end{aligned} $$ $$ \begin{aligned} \vec r(1.0)&=4\i+2\sqrt2\j\ut{m}\approx 4.0\i+ 2.8\j\ut{m}\\ \vec r(2.0)&=8\i+4\j\ut{m}=8.0\i+4.0\j\ut{m}\\ \vec r(3.0)&=12\i+2\sqrt2\j\ut{m}\approx 12\i+ 2.8\j\ut{m}\\ \vec r(4.0)&=16\i+0\j\ut{m} \end{aligned} $$ $..

$$ \begin{cases} v&=8.50\ut{m/s}\\ a_R&=4.00\ut{m/s^2}\\ \end{cases} $$ $$\ab{a}$$ $$a_R=\frac{v^2}{R},$$ $$ \begin{aligned} R&=\frac{v^2}{a_R}\\ &=\frac{289}{16}\ut{m}\\ &=18.0625\ut{m}\\ &\approx 18.1\ut{m}\\ \end{aligned} $$ $$\ab{b}$$ $$v=\frac{2\pi R}{T},$$ $$ \begin{aligned} T&=\frac{2\pi R}{v}\\ &=\frac{17\pi}{4}\ut{s}\\ &\approx 13.35176877775662\ut{s}\\ &\approx 13.4\ut{s}\\ \end{aligne..

$$ \begin{cases} v_0&=82\ut{m/s}, \theta_0=45\degree\\ \Delta x_1 &= 686\ut{m}\\ h&=40.0\ut{m} \end{cases} $$ $$ \begin{aligned} S&=v_0t+\frac{1}{2}at^2,\\ 0&=v_{y0}t+\frac{1}{2}(-g)t^2\\ &=v_0\sin\theta-\frac{1}{2}gt\\ t&=\frac{2v_0}{g}\sin\theta \end{aligned} $$ $$ \begin{aligned} \Delta x_1 &= v_x t\\ &= v_0\cos\theta \(\frac{2v_0}{g}\sin\theta\)\\ &=\frac{{v_0}^2}{g}\sin (2\theta )\\ &=\frac..

$$ \begin{cases} \vec v_{E}&= 8.0\j\ut{m/s}\\ y_0 &= 22\ut{m}\\ \vec v_{0B\larr E}&= 18\j\ut{m/s}\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} \vec v_{B0}&=\vec v_{0B\larr E}+\vec v_{E}\\ &=18\j+8.0\j\\ &=26\j\\ \end{aligned} $$ $$ \begin{aligned} 2aS&=v^2-{v_0}^2,\\ 2(-g)(h)&=(0)^2-(v_{By0})^2\\ 2gh&=(18)^2\\ \end{aligned} $$ $$ \begin{aligned} h&=\frac{162}{g}\\ &\approx..

$$ \begin{cases} \vec r_1 &= 6.0\i-5.0\j+2.0\k\ut{m}\\ \vec r_2 &= -4.0\i+6.0\j+2.0\k\ut{m}\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} \Delta \vec r&=\vec r_2-\vec r_1\\ &=10\i-11\j\ut{m} \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} \Delta \vec r&=\vec r_2-\vec r_1\\ &=10\i-11\j\ut{m}\\ \end{aligned} $$ $$ \begin{aligned} C_1(11x+10y)+C_2z=0 \end{aligned} $$

$$ \begin{cases} A:\text{Ship}\\ B:\text{Water} \end{cases} $$ $$ \begin{cases} \Delta x &= 8.0\ut{km}\\ \vec v_{B}&=2.6\ut{km/h}\j\\ v_{A\larr B}&=8.0\ut{km/h}\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} \vec v_{A\larr B}&=8\i\ut{km/h},\\ \vec v_A &= \vec v_{A\larr B}+\vec v_B\\ &= 8\i+2.6\j\\ \end{aligned} $$ $$ \begin{aligned} \theta_A&=\tan^{-1}\frac{2.6}{8}\\ &\approx 0.3142318990843383\..

$$ \begin{cases} H:\text{Helicopter}\\ B:\text{Box} \end{cases} $$ $$ \begin{cases} h_{H}&=11.6\ut{m}\\ \vec v_H&=6.20\ut{m/s}\i\\ \vec v_{B0\larr H}&=-15.0\ut{m/s}\i \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} \vec v_{B0}&=\vec v_{B0\larr H}+\vec v_H\\ &=-15.0\ut{m/s}\i+6.20\ut{m/s}\i\\ &=8.8\ut{m/s}\i \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} S&=v_0t+\frac{1}{2}at^2,\\ \Delta y&=(0)t+\fr..

$$ \begin{cases} \vec v_0&=2.5\times10^6\ut{m/s}\\ \Delta x &= 3.3\ut{m}\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} t &= \frac{\Delta x}{v_x} \\ &= \frac{3.3}{v_x} \\ \end{aligned} $$ $$ \begin{aligned} S&=v_0t+\frac{1}{2}at^2,\\ \Delta y&=(0)t+\frac{1}{2}(-g)t^2\\ &=-\frac{1}{2}g\(\frac{3.3}{v_x}\)^2\\ &=-\frac{1089g}{200{v_x}^2}\\ \end{aligned} $$ $$ \begin{aligned} \a..