4-67 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} T&=5.00\ut{s}\\ \vec r &=2.00\i-3.00\j\ut{m} \end{cases} $$ $$ \begin{aligned} R&=\sqrt{2^2+(-3)^2}\\ &=\sqrt{13} \end{aligned} $$ $$ \begin{aligned} v&=\frac{2\pi R}{T}\\ &=\frac{2\sqrt{13}\pi}{5}\ut{m/s}\\ \end{aligned} $$ $$ \begin{aligned} \frac{\Delta y}{\Delta x}\cdot\frac{v_y}{v_x}&=-1\\ \frac{v_y}{v_x}&=\frac{2}{3}=\frac{-2}{-3}\\ \end{aligned} $$ $$ \begin{aligned} \vec v &=\frac{2\sqrt{13}\pi}{5}\cdot\frac{-3}{\sqrt{13}}\i+\frac{2\sqrt{13}\pi}{5}\cdot\frac{-2}{\sqrt{13}}\j\ut{m/s}\\ &=-\frac{6\pi}{5}\i-\frac{4\pi}{5}\j\ut{m/s}\\ &\approx -3.77\i-2.51\j\ut{m/s} \end{aligned} $$