솔루션피아

$$ \begin{cases} p:\text{Plane in Wind}\\ w:\text{Wind}\\ q:\text{Plane on Land}\\ \end{cases} $$ $$ \begin{cases} v_p&=p=125\ut{mi/h}\\ v_w&=w=55.0\ut{mi/h}\\ \vec v_q&=\vec q=125\j\ut{mi/h}\\ \end{cases} $$ $$ \begin{aligned} \vec p&=\vec q-\vec w\\ \vec q&=\vec p+\vec w\\ 125\j&=\vec p+\vec w\\ \end{aligned} $$ $$ \begin{cases} p_x+w_x&=0\\ p_y+w_y&=125\\ {p_x}^2+{p_y}^2&=125\\ {w_x}^2+{w_y}^..

$$ \begin{cases} R_t&=(x,y)\ut{m}\\ R_0&=(0,2)\ut{m}\\ R_{0.5}&=(5,6)\ut{m}\\ R_{1}&=(10,8)\ut{m}\\ R_{1.5}&=(15,8)\ut{m}\\ R_{2}&=(20,6)\ut{m}\\ R_{2.5}&=(25,2)\ut{m}\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} v_x &=\frac{\Delta x}{\Delta t}\\ &=\frac{10}{1}\ut{m}\\ &=10\ut{m}\\ \end{aligned} $$ $$ \begin{aligned} v_y&=\frac{\Delta y}{\Delta t}\\ v_{0\rarr0.5}&=\frac{4}{0.5}=8\ut{m/s}\\ v_{..

$$ \begin{cases} H&=25\ut{m}\\ v_1&=4.00v_0\\ g&=9.80665\ut{m/s^2}\\ \end{cases} $$ $$ \begin{aligned} v_0&=v_x, \end{aligned} $$ $$ \begin{aligned} 2aS&=v^2-{v_0}^2,\\ 2(-g)(-25)&={v_{y1}}^2-{0}^2\\ 50g&={v_{y1}}^2\\ \end{aligned} $$ $$ \begin{aligned} {v_1}^2&={v_x}^2+{v_{y1}}^2\\ (4v_0)^2&={v_0}^2+50g\\ \end{aligned} $$ $$ \begin{aligned} v_0&=\sqrt{\frac{10g}{3}}\\ &\approx 5.717414917017422..

$$ \begin{cases} A:\text{Walk}\\ B:\text{Travelator}\\ C:\text{Walk+Travelator} \end{cases} $$ $$ \begin{cases} t_A&=180\ut{s}\\ t_B&=60.0\ut{s}\\ \end{cases} $$ $$ \begin{aligned} v_A&=\frac{S}{t_A}\\ v_B&=\frac{S}{t_B}\\ t_C&=\frac{S}{v_C}\\ &=\frac{S}{v_A+v_B}\\ &=\frac{S}{\frac{S}{t_A}+\frac{S}{t_B}}\\ &=\frac{1}{\frac{1}{180}+\frac{1}{60}}\\ &=45\ut{s} \end{aligned} $$

$$ \begin{cases} v_x&=12.0\ut{m/s}\\g&=9.80665\ut{m/s^2}\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} v&=v_0+at,\\ v_y&=v_{y0}-gt\\ v_y&=0-gt\\ \end{aligned} $$ $$ \begin{aligned} v_y(t)&=-gt\\ \vec v(t)&=12\i-gt\j \end{aligned} $$ $$v(t)=\sqrt{12^2+(gt)^2}$$ $$ \begin{aligned} v(-1.2)&=\sqrt{12^2+(-1.2g)^2}\\ &\approx 16.80730059469396\ut{m/s}\\ &\approx 16.8\ut{m/s}\\ \end{aligned} $$ $$\ab{..

$$ \begin{cases} \vec v_0 &= 8.00\times10^8\i\ut{cm/s}\\ \Delta x &= 2.00\ut{cm}\\ \vec a&=-6.70\times10^{16}\j\ut{cm/s^2}\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} t&=\frac{\Delta x}{v_x}\\ &=\frac{2}{8\times10^8}\ut{s}\\ &=2.50\times10^{-9}\ut{s} \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} S&=v_0t+\frac{1}{2}at^2,\\ \end{aligned} $$ $$ \begin{aligned} \Delta y&=v_{y0}t+\frac{1}{2}a_yt^..

$$ \begin{cases} A:\text{Walk Case}\\ B:\text{Escalator Case}\\ C:\text{Walk and Escalator} \end{cases} $$ $$ \begin{cases} t_A&=80\ut{s}\\ t_B&=45\ut{s} \end{cases} $$ $$\ab{a}$$ $$ \begin{cases} v_A&=\cfrac{S}{t_A}\\ v_B&=\cfrac{S}{t_B}\\ \end{cases} $$ $$ \begin{aligned} t_C &= \frac{S}{v_A+v_B}\\ &= \frac{S}{\frac{S}{t_A}+\frac{S}{t_B}}\\ &= \frac{1}{\frac{1}{t_A}+\frac{1}{t_B}}\\ &= \frac{1..

$$ \begin{cases} r_1 &=720\ut{m}\\ \theta_1&=40\degree\\ r_2&=1580\ut{m}\\ \Delta \theta&=123\degree \end{cases} $$ $$ \begin{aligned} \theta_2&=40\degree+123\degree\\ &=163\degree \end{aligned} $$ $$ \begin{cases} \vec r_1 &= 720\cos40\degree\i+ 720\sin40\degree\j\\ \vec r_2 &=1580\cos163\degree\i+1580\sin163\degree\j\\ \end{cases} $$ $$ \begin{aligned} \Delta \vec r &=\vec r_2 - \vec r_1,\\ &=..

$$ \begin{cases} \vec v_0&=10\j\ut{m/s}\\ \vec a&=6.0\i+2.0\j\ut{m/s^2}\\ \end{cases} $$ $$ \begin{aligned} \vec v &= \vec v_0+\Delta \vec v\\ &= 10\j+\int_0^t\vec a\dd t\\ &= 10\j+\int_0^t6\i+2\j\dd t\\ &= 6t\i+\(10+2t\)\j\\ \end{aligned} $$ $$ \begin{aligned} \vec r &= \vec r_0+\Delta \vec r\\ &= 0+\int_0^t\vec v\dd t\\ &= \int_0^t6t\i+\(10+2t\)\j\dd t\\ &=3t^2\i+\(10t+t^2\)\j \end{aligned} $$..

$$ \begin{cases} \vec v_0&=4.50\i\ut{m/s}\\ \vec a&=1.2\j\ut{m/s^2}\\ t&=4.70\ut{s} \end{cases} $$ $$ \begin{aligned} \vec v(t)&=\vec v_0+\Delta \vec v\\ &=\vec v_0+\int_0^{t}\vec a\dd t\\ &=4.50\i+\int_0^{t}1.2\j\dd t\\ &=4.50\i+1.2t\j\\ \end{aligned} $$ $$\ab{a}$$ $$ \begin{aligned} \vec v(4.70)&=4.50\i+1.2(4.7)\j\ut{m/s}\\ &=4.50\i+5.64\j\ut{m/s}\\ &\approx 4.5\i+5.6\j\ut{m/s}\\ \end{aligned}..