2-34 할리데이 10판 솔루션 일반물리학

$$ \begin{cases} x_{R0} &= 0\ut{m} \\ x_{G0} &= 220\ut{m} \\ a_G &= Const. \\ a_R &= 0 \end{cases}$$ $$ \begin{aligned} S &= vt, \\ S_{R} &= v_{R}t \\ t &= \frac{S_{R}}{v_{R}} \end{aligned} $$ $$ (\text{Case A}) $$ $$ \begin{aligned} v_{RA} &= 20.0\ut{km/h} \\ &= 20.0\ut{km/h}\frac{1000\ut{m}}{1\ut{km}}\frac{1\ut{h}}{3600\ut{s}} \\ &= \frac{50}{9}\ut{m/s} \\ \end{aligned} $$ $$A\begin{cases} v_{RA} &= \frac{50}{9}\ut{m/s} \\ S_{RA} &= 44.5\ut{m} \\ S_{GA} &= x_{G0}-S_{RA} = 220-44.5 =175.5\ut{m} \\ t_A &= \frac{S_{RA}}{v_{RA}}=44.5\frac{9}{50}=8.01\ut{s} \end{cases}$$ $$ (\text{Case B}) $$ $$ \begin{aligned} v_{RB} &= 40.0\ut{km/h} \\ &= 40.0\ut{km/h}\frac{1000\ut{m}}{1\ut{km}}\frac{1\ut{h}}{3600\ut{s}} \\ &= \frac{100}{9}\ut{m/s} \end{aligned} $$ $$ B\begin{cases} v_{RB} &= \frac{100}{9}\ut{m/s} \\ S_{RB} &= 77.9\ut{m} \\ S_{GB} &= x_{G0}-S_{RB}=220-77.9 =142.1\ut{m} \\ t_B &= \frac{S_{RB}}{v_{RB}}=77.9\frac{9}{100}=7.011\ut{s} \end{cases}$$ $$ (\text{Make System Of Equations Case A,B}) $$ $$ \begin{aligned} S &= v_0t+\frac{1}{2}at^2, \\ S_{G} &= \overset{x}{v_{G0}}t+\frac{1}{2}\overset{y}{a_G}t^2 \end{aligned} $$ $$(\text{OverSet x,y Means Unknown Value}) $$ $$ \begin{cases} S_{GA} &= \overset{x}{v_{G0}}t_A+\frac{1}{2}\overset{y}{a_G}t_A^2 \\ S_{GB} &= \overset{x}{v_{G0}}t_B+\frac{1}{2}\overset{y}{a_G}t_B^2 \end{cases} $$ $$ \begin{aligned} v_{G0}&= -\frac{S_{GA} t_B^2-S_{GB} t_A^2}{t_A t_B (t_A-t_B)} \\ a_G&= \frac{2 (S_{GA} t_B-S_{GB} t_A)}{t_A t_B (t_A-t_B)} \end{aligned} $$ $$(\text{Input Values})$$ $$\begin{cases} S_{GA} & =175.5\ut{m} \\ S_{GB} &=142.1\ut{m} \\ t_A &=8.01\ut{s} \\ t_B &= 7.011\ut{s} \end{cases} $$ $$v_{g0} = \frac{605681450}{69261669}\ut{m/s} $$ $$ a_G = \frac{2049100000}{623355021}\ut{m/s^2} $$
(a) $$ \begin{aligned} v_{G0} &= ? \\ &=\frac{605681450}{69261669}\ut{m/s} \\ &\approx 8.744828976038681\ut{m/s} \\ &\approx 8.74\ut{m/s} \end{aligned} $$
(b) $$ \begin{aligned} a_G &= ? \\ &= \frac{2049100000}{623355021}\ut{m/s^2} \\ &\approx 3.287211831089109\ut{m/s^2} \\ &\approx 3.29\ut{m/s^2} \end{aligned} $$