솔루션피아

$$ \begin{cases} \Delta \vec r &= 2.0\i-4.0\j+5.0\k\\ \vec r&=3.0\j-4.0\k\\ \end{cases} $$ $$ \begin{aligned} \vec r &= \vec r_0 + \Delta \vec r\\ \vec r_0 &= \vec r - \Delta \vec r\\ &= \(3.0\j-4.0\k\)-\(2.0\i-4.0\j+5.0\k\)\\ &=-2.0\i+7.0\j-9.0\k \end{aligned} $$

$$ \begin{cases} v_0&=22\ut{m/s},\theta_0=60\degree\\ t_1&=1.2\ut{s}\\ \end{cases} $$ $$\ab{a,b,c}$$ $$v=v_0+at,$$ $$ \begin{aligned} v_{y1}&=22\sin60\degree+(-g)(1.2)\\ &=11\sqrt{3}-\frac{6}{5}g\\ \end{aligned} $$ $$ \begin{aligned} \vec v_1&=20\cos60\degree\i+\(11\sqrt{3}-\frac{6}{5}g\)\j\\ &=10\i+\(11\sqrt{3}-\frac{6}{5}g\)\j\\ \end{aligned} $$ $$\ab{a}$$ $$ \begin{aligned} v_1 &= \sqrt{10^2+..

$$ \begin{cases} R&=20.0\ut{cm}=0.2\ut{m}\\ T&=5.00\ut{ms}=5\times10^{-3}\ut{s}\\ h&=1.20\ut{m}\\ d&=3.50\ut{m}\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$[\text{get }\theta_0]$$ $$ \begin{aligned} \theta_{5\text{o'clock}\larr x+}&= -\frac{2}{12}\cdot2\pi\ut{rad}\\ &=-\frac{\pi}{3}\ut{rad}\\ \end{aligned} $$ $$\theta_{5\text{o'clock}\larr x+}\perp\theta_0,$$ $$ \begin{aligned} \theta_0&=-\frac{\pi}..

$$ \begin{cases} \Delta x_1&=8.09\ut{m}\\ g_1&=9.8128\ut{m/s^2}\\ g_2&=9.7999\ut{m/s^2}\\ \end{cases} $$ $$S=v_0t+\frac{1}{2}at^2,$$ $$ \begin{aligned} 0&=(v_0\sin\theta)t+\frac{1}{2}(-g)t^2\\ 0&=v_0\sin\theta-\frac{1}{2}gt\\ \end{aligned} $$ $$\therefore t=\frac{2v_0}{g}\sin\theta$$ $$\Delta x = v_x t,$$ $$ \begin{aligned} \Delta x&= v_0\cos\theta \cdot \(\frac{2v_0}{g}\sin\theta\)\\ &=\frac{{v..

$$ \begin{cases} t_1&=3.2\ut{s}\\ t_2&=t_1+2.9\ut{s}\\ x_2&=86.0\ut{m}\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} S&=vt-\frac{1}{2}at^2,\\ \Delta y_{0\rarr1}&=(0)t-\frac{1}{2}(-g)(3.2)^2\\ &=\frac{128}{25}g\\ &=\frac{784532}{15625}\ut{m}\\ &= 50.210048\ut{m}\\ &\approx 50\ut{m}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} S&=v_0t+\frac{1}{2}at^2,\\ \Delta y_{1\rarr2} &=(0)t+\frac{1}{2}(-..

$$ \begin{cases} R&=4.5\ut{m}\\ a_R&=6.5g\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$\ab{a}$$ $$a=\frac{v^2}{R},$$ $$ \begin{aligned} v&=\sqrt{aR}\\ &=\sqrt{(6.5g)(4.5)}\\ &=\frac{3 }{2}\sqrt{13g}\\ &=\frac{3 }{200}\sqrt{\frac{2549729}{2}}\ut{m/s^2}\\ &\approx 16.93648465591369\ut{m/s^2}\\ &\approx 17\ut{m/s^2}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} f &=\frac{\omega}{2\pi}\\ &= \frac{v}{2..

$$ \begin{cases} \vec r_A&=0 &\\ t_{A\rarr B}&=45.0\ut{min},&\vec r_B=500\i\ut{km}\\ t_{B\rarr C}&=1.50\ut{h},&\vec r_C=-1100\j\ut{km}\\ \end{cases} $$ $$\Sigma \vec r = \(500\i-1100\j\)\ut{km}$$ $$\ab{a}$$ $$ \begin{aligned} r&= \sqrt{500^2+1100^2}\\ &=100\sqrt{146}\ut{km}\\ &\approx 1208.304597359457\ut{km}\\ &\approx 1.21\times10^3\ut{km}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} \thet..

$$ \begin{cases} v_x &= 15.0\ut{m/s}\\ t&=0.140\ut{s}\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} S&=v_0t+\frac{1}{2}at^2\\ -\Delta y&=(0)t+\frac{1}{2}(-g)(0.14)^2\\ \Delta y&=0.09610517\ut{m}\\ &= 9.610517\ut{cm}\\ &\approx 9.61\ut{cm}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} \Delta x &= v_x t\\ &=15.0\ut{m/s}\cdot0.140\ut{s}\\ &= 2.1\ut{m} &= 2.10\ut{m} \end{ali..

$$ \begin{cases} h_1&=10.2\ut{m}\\ \vec v_1&=\(8.90\i+6.70\j\)\ut{m/s}\\ g&=9.80665\ut{m/s^2}\\ \end{cases} $$ $$\ab{a}$$ $$2aS=v^2-{v_0}^2,$$ $$ \begin{cases} 2(-g)(h_1)&=(v_{y1})^2-{v_{y0}}^2\\ 2(-g)(h_{\max})&=(v_{y\max})^2-{v_{y0}}^2\\ \end{cases} $$ $$ \begin{aligned} h_{\max}&=\frac{2 g h_1-(v_{y\max})^2+(v_{y1})^2}{2 g}\\ &=\frac{2 g (10.2)-0^2+(6.7)^2}{2 g}\\ &=\frac{4489}{200 g}+\frac{5..

$$ \begin{cases} v_a&=23.0\ut{m/s}\\ v_b&=33.6\ut{m/s}\\g&=9.80665\ut{m/s^2}\\ \end{cases} $$ $$\ab{a}$$ $$v_a = v_x,$$ $$ \begin{aligned} \Delta x &= v_x t\\ &=v_a t\\ &=23\ut{m/s}\cdot5\ut{s}\\ &=115\ut{m} \end{aligned} $$ $$\ab{b}$$ $${v_x}^2+{v_y}^2=v^2,$$ $$ \begin{aligned} 2aS&=v^2-{v_0}^2\\ 2(-g)(H)&=0^2-{v_{y0}}^2\\ 2gH&={v_{y0}}^2\\ \end{aligned} $$ $$ \begin{aligned} H&=\frac{v^2-{v_x}..