솔루션피아

$$ \begin{cases} \Delta t &= 3.15\ut{h}\\ \Delta \vec r &= 11.2\i+24.5\j+2.88\k\ut{km} \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} \bar v &= \frac{\Delta r}{\Delta t}\\ &= \frac{\sqrt{11.2^2+24.5^2+2.88^2}}{3.15}\ut{km/h}\\ &=\frac{2\sqrt{1834961}}{315}\ut{km/h}\\ &\approx 8.600681416985678\ut{km/h}\\ &\approx 8.60\ut{km/h}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} \vec n &= 0\i+0j+1\k,\..

$$ \begin{cases} T&=5.00\ut{s}\\ \vec r &=2.00\i-3.00\j\ut{m} \end{cases} $$ $$ \begin{aligned} R&=\sqrt{2^2+(-3)^2}\\ &=\sqrt{13} \end{aligned} $$ $$ \begin{aligned} v&=\frac{2\pi R}{T}\\ &=\frac{2\sqrt{13}\pi}{5}\ut{m/s}\\ \end{aligned} $$ $$ \begin{aligned} \frac{\Delta y}{\Delta x}\cdot\frac{v_y}{v_x}&=-1\\ \frac{v_y}{v_x}&=\frac{2}{3}=\frac{-2}{-3}\\ \end{aligned} $$ $$ \begin{aligned} \vec..

$$ \begin{cases} \vec v_3&=3.00\i+4.00\j\ut{m/s}\\ \vec v_5&=-3.00\i-4.00\j\ut{m/s}\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} \frac{T}{2}&=2\ut{s},\\ T&=4\ut{s} \end{aligned} $$ $$ \begin{aligned} v&=\sqrt{3^2+4^2}\ut{m/s}\\ &=5\ut{m/s}\\ \end{aligned} $$ $$ \begin{aligned} v&=\frac{2\pi R}{T},\\ R&=\frac{vT}{2\pi}\\ &=\frac{10}{\pi}\ut{m} \end{aligned} $$ $$ \begin{aligned} a&=\frac{v^2}{R..

$$ \begin{cases} \vec v_0&=5.02\i-9.24\j\ut{m/s}\\ \Delta t &= 3.00\ut{s}\\ \vec v_1&=0 \end{cases} $$ $$ \begin{aligned} \vec a &= \frac{\Delta \vec v}{\Delta t}\\ &= \frac{\vec v_1-\vec v_0}{\Delta t}\\ &= \frac{\vec v_1}{\Delta t}\\ &= \frac{5.02\i-9.24\j}{3}\ut{m/s^2}\\ &= \frac{251}{150}\i-\frac{77}{25}\j\ut{m/s^2}\\ &\approx 1.67\i-3.08\j\ut{m/s^2} \end{aligned} $$

$$ \begin{cases} A:(5.00,3.00)\ut{m}\\ B:(12.0,18.0)\ut{m}\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} &\text{dirction of } \vec a \\ &=\text{dirction of } \vec v \\ &=\text{dirction of } \Delta\vec x \end{aligned} $$ $$ \begin{aligned} \Ans &= \frac{a_y}{a_x}\\ &= \frac{v_y}{v_x}\\ &= \frac{\Delta y}{\Delta x}\\ &= \frac{18-3}{12-5}\\ &= \frac{15}{7}\\ &\approx 2.142857142857143\\ &\approx 2..

$$ \begin{cases} a_R &= 6.00\times10^{14}\ut{m/s^2}\\ R &= 18.0\ut{cm}\\ \end{cases} $$ $$\ab{a}$$ $$a_R=\frac{v^2}{R},$$ $$ \begin{aligned} v&=\sqrt{Ra_R}\\ &=6\sqrt3\times10^6\ut{m/s}\\ &\approx 1.039230484541326\times10^7\ut{m/s}\\ &\approx 1.04\times10^7\ut{m/s}\\ \end{aligned} $$ $$\ab{b}$$ $$v=\frac{2\pi R}{T},$$ $$ \begin{aligned} T&=\frac{2\pi R}{v}\\ &= \frac{2\pi R}{\sqrt{Ra_R}}\\ &=\f..

$$ \begin{cases} \Delta x &= 45\ut{m}\\ \Delta y &= 2.9\ut{cm}\\ g&= 9.80665\ut{m/s^2}\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} S&=v_0t+\frac{1}{2}at^2,\\ -\Delta y &= v_{y0}t+\frac{1}{2}(-g)t^2\\ &= (0)t-\frac{1}{2}gt^2\\ \end{aligned} $$ $$ \begin{aligned} t&= \sqrt{\frac{2\Delta y}{g}}\\ &\approx 0.07690483752841551\ut{s}\\ &\approx 0.077\ut{s}\\ &\approx 77\ut{ms}\\ \end{aligned} $$ $$..

$$ \begin{cases} a_{\max}&=23.0g\\ g&=9.80665\ut{m/s^2}\\ v&=0.00200c\\ c&=299792458\ut{m/s} \end{cases} $$ $$\ab{a}$$ $$a=\frac{v^2}{R},$$ $$ \begin{aligned} R&=\frac{v^2}{a}\\ &=\frac{(0.00200c)^2}{23g}\\ &=\frac{c^2}{5750000g}\\ &\approx 1.5938699604448848\times 10^9\ut{m}\\ &\approx 1.59\times 10^9\ut{m}\\ \end{aligned} $$ $$\ab{b}$$ $$v=\frac{2\pi R}{T},$$ $$ \begin{aligned} \Ans&=\frac{T}{..

$$ \begin{cases} v_0&=12.0\ut{m/s},\theta_0=-15.0\degree\\ t_1 &= 1.51\ut{s} \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} v_x &= 12\cos(-15\degree)\\ &=3 \sqrt{2} \(1+\sqrt{3}\)\ut{m/s}\\ \end{aligned} $$ $$ \begin{aligned} \Delta x &= v_x t\\ &=3 \sqrt{2} \(1+\sqrt{3}\)\cdot 1.51\\ &=\frac{453 \(1+\sqrt{3}\)}{50 \sqrt{2}}\ut{m}\\ &\approx 17.50257597235792\ut{m}\\ &\approx 17.5\ut{m}\\ \end{ali..

$$ \begin{cases} \vec r(0)&=0\i+3.0\j\ut{ft}\\ \vec r(0.25)&=8.0\i+7.0\j\ut{ft}\\ \vec r(0.50)&=16\i+9.0\j\ut{ft}\\ \vec r(0.75)&=24\i+9.0\j\ut{ft}\\ \vec r(1.00)&=32\i+7.0\j\ut{ft}\\ \vec r(1.25)&=40\i+3.0\j\ut{ft}\\ \end{cases} $$ $$ \begin{aligned} v_{x0\rarr0.25} &= \frac{8.0\ut{ft}}{0.25\ut{s}}=32\ut{ft/s}\\ v_{x0.25\rarr0.50} &= \frac{8.0\ut{ft}}{0.25\ut{s}}=32\ut{ft/s}\\ v_{x0.50\rarr0.75..