8-58 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} mg&=620\ut{N}\\ v_0&=0\\ a&=\Cons\\ \Delta S&=6.5\ut{m}\\ \Delta t&=1.6\ut{s}\\ \end{cases} $$ $$\ab{a}$$ $$S=\frac{1}{2}\(v+v_0\)t,$$ $$ \begin{aligned} v&=\frac{2S}{t}-v_0\\ &=\frac{2S}{t}\\ &=\frac{65}{8}\ut{m/s}\\ &=8.125\ut{m/s}\\ &\approx 8.1\ut{m/s}\\ \end{aligned} $$ $$\ab{b}$$ $$\KE=\frac{1}{2}mv^2,$$ $$ \begin{aligned} \KE&=\frac{1}{2}m\(\frac{2S}{t}\)^2\\ &=\frac{2mS^2}{t^2}\\ &=\frac{654875}{32 g}\\ &\approx 2086.8332967935025\ut{J}\\ &\approx 2.1\times10^3\ut{J}\\ &\approx 2.1\ut{kJ}\\ \end{aligned} $$ $$\ab{c}$$ $$ \begin{aligned} P&=\frac{W}{t}\\ &=\frac{\Delta \KE}{t}\\ &=\frac{\KE}{t}\\ &=\frac{2mS^2}{t^3}\\ &=\frac{3274375}{256 g}\\ &\approx 1304.270810495939\ut{W}\\ &\approx 1.3\times10^3\ut{W}\\ &\approx 1.3\ut{kW}\\ \end{aligned} $$