9-7 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} \vec v_0&=v_0\i\\ v_{A1}&=3.50\ut{m/s}, \theta_{A1}&=22.0\degree\\ v_{B1}&=2.00\ut{m/s} \end{cases} $$ $$ \begin{cases} \vec v_{A1}&=3.5\cos22\degree\i+3.5\sin22\degree\j\\ \vec v_{B1}&=2\cos\theta\i+2\sin\theta\j\\ \end{cases} $$ $$\Delta \Sigma \vec P=0,$$ $$ \begin{aligned} \vec P_0&=\vec P_{A1}+\vec P_{B1}\\ m\vec v_0&=m\vec v_{A1}+m\vec v_{B1}\\ \vec v_0&=\vec v_{A1}+\vec v_{B1}\\ \end{aligned} $$ $$ \begin{aligned} v_0\i&=(3.5\cos22\degree\i+3.5\sin22\degree\j)\\ &~~~~~+(2\cos\theta\i+2\sin\theta\j)\\ &=(3.5\cos22\degree+2\cos\theta)\i\\ &~~~~~+(3.5\sin22\degree+2\sin\theta)\j\\ \end{aligned} $$ $$ \begin{cases} v_0&=3.5\cos22\degree+2\cos\theta\\ 0&=3.5\sin22\degree+2\sin\theta \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} \theta &= -\sin ^{-1}\(\frac{7}{4}\sin 22\degree\)\\ &\approx -0.7149260006297955\ut{rad}\\ &\approx -0.715\ut{rad}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} v_0&=3.5\cos22\degree+2\cos\theta\\ &=3.5\cos22\degree+2\cos\bra{-\sin ^{-1}\(\frac{7}{4}\sin 22\degree\)}\\ &\approx 4.755426999823815\ut{m/s}\\ &\approx 4.76\ut{m/s}\\ \end{aligned} $$ $$\ab{c}$$ $$ \begin{cases} \Sigma \KE_f&=\frac{1}{2}m{v_{A1}}^2+\frac{1}{2}m{v_{B1}}^2\\ \KE_i&=\frac{1}{2}m{v_0}^2\\ \end{cases} $$ $$ \begin{aligned} \frac{\Sigma \KE_f}{\KE_i}&=\frac{\frac{1}{2}m{v_{A1}}^2+\frac{1}{2}m{v_{B1}}^2}{\frac{1}{2}m{v_0}^2}\\ &=\frac{{v_{A1}}^2+{v_{B1}}^2}{{v_0}^2}\\ &\approx 0.7185786785926022 \ne 1\\ \end{aligned} $$ $$\text{Not Conservation}$$