8-59 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} m&=1.88\ut{kg}\\ \theta&=34.0\degree\\ v_0&=24.0\ut{m/s}\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} \KE&=\frac{1}{2}m{v}^2,\\ &=\frac{13536}{25}\ut{J}\\ &=541.44\ut{J}\\ &\approx 541\ut{J}\\ \end{aligned} $$ $$\ab{b}$$ $$v_f=v_x=v\cos\theta$$ $$\Sigma \Delta E=0,$$ $$\Delta \KE+\Delta \GE=0$$ $$ \begin{aligned} \Delta \GE&=-\Delta \KE\\ &=-\Delta \(\frac{1}{2}m{v}^2\)\\ &=-\frac{1}{2}m\Delta \({v}^2\)\\ &=\frac{1}{2}m \({v_i}^2-{v_f}^2\)\\ &=\frac{1}{2}m \bra{{v_i}^2-{(v_i\cos\theta)}^2}\\ &=\frac{1}{2}m{v_i}^2\sin^2\theta\\ &\approx 169.30650303044436\ut{J}\\ &\approx 169\ut{J}\\ \end{aligned} $$ $$\ab{c}$$ $$ \begin{aligned} \Delta \GE &=\frac{1}{2}m{v_i}^2\sin^2\theta\\ mg\Delta h&=\frac{1}{2}m{v_i}^2\sin^2\theta\\ \end{aligned} $$ $$ \begin{aligned} \Delta h&=\frac{{v_i}^2}{2g}\sin^2\theta\\ &\approx 9.183222665039407\ut{m}\\ &\approx 9.18\ut{m}\\ \end{aligned} $$