8-22 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} 0:\text{Start}\\ 1:h_{\max}\\ 2:\Delta h = -3.0\ut{m} \end{cases} $$ $$ \begin{cases} m&=88\ut{g}\\ \theta&=30\degree\\ v_0&=8.0\ut{m/s}\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$ \begin{aligned} \vec v_0 &= v_0\cos\theta\i+v_0\sin\theta\j,\\ \end{aligned} $$ $$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \end{cases} $$ $$\ab{a}$$ $$\vec v_1= v_0\cos\theta\i\ut{m/s}$$ $$ \begin{aligned} \KE_1&=\frac{1}{2}m{v_1}^2\\ &=\frac{1}{2}m(v_0\cos\theta)^2\\ &=\frac{264}{125}\ut{J}\\ &=2.112\ut{J}\\ &\approx 2.1\ut{J}\\ \end{aligned} $$ $$\ab{b}$$ $$\Sigma E_0=\Sigma E_2,$$ $$ \begin{aligned} \KE_0+\GE_0&=\KE_2+\GE_2\\ \KE_2&=\KE_0-\Delta \GE\\ \frac{1}{2}m{v_2}^2&=\frac{1}{2}m{v_0}^2-mg\Delta h\\ v_2&=\sqrt{{v_0}^2-2g\Delta h}\\ &=\sqrt{64+6g}\\ &\approx 11.083316290713714\ut{m/s}\\ &\approx 11\ut{m/s}\\ \end{aligned} $$ $$\ab{c}$$ $$v_2=\sqrt{{v_0}^2-2g\Delta h},$$ $$\Cons \text{ about } m$$ $$\ab{d}$$ $$v_2=\sqrt{{v_0}^2-2g\Delta h},$$ $$\Cons \text{ about } \theta$$