2-13 할리데이 11판 솔루션 일반물리학

$$\begin{cases} a&=-g=-9.80665\ut{m/s^s}\\ v_0&=0\\ t_1&=50\ut{ms}=0.05\ut{s}\\ t_2&=100\ut{ms}=2t_1\\ t_3&=150\ut{ms}=3t_1\\ t_4&=200\ut{ms}=4t_1\\ t_5&=250\ut{ms}=5t_1 \end{cases}$$ $$$$ $$\begin{aligned} S_k&=v_0t+\frac{1}{2}at^2,\\ &=\frac{1}{2}g(t_k)^2\\ \end{aligned}$$ $$\ab{a}$$ $$\begin{aligned} S_{1}&=\frac{1}{2}gt_1^2\\ &=\frac{1}{2}(9.80665\ut{m/s^2})(0.05\ut{s})^2\\ &=\frac{196133}{16000000}\ut{m}\\ &=0.0122583125\ut{m}\\ &=12.2583125\ut{mm}\\ &\approx12\ut{mm} \end{aligned}$$ $$\ab{b}$$ $$\begin{aligned} \Ans_k&=\frac{S_k}{S_1}\\ &=\frac{\frac{1}{2}g(t_k)^2}{\frac{1}{2}gt_1^2}\\ &=\(\frac{t_k}{t_1}\)^2\\ &=\(\frac{kt_1}{t_1}\)^2\\ &=\(k\)^2\\ \end{aligned}$$ $$\Ans_2=2^2=4$$ $$\ab{c}$$ $$\Ans_3=3^2=9$$ $$\ab{d}$$ $$\Ans_4=4^2=16$$ $$\ab{e}$$ $$\Ans_5=5^2=25$$