2-8 할리데이 10판 솔루션 일반물리학

$$ \begin{cases} v_w &= 3.50\ut{m/s} \\ d &= 0.25\ut{m} \\ L &= 1.75\ut{m} \end{cases} $$
(a) $$ \put \begin{cases} n &= \text{Human On Wall Number}\ut{EA} \\ t_k &= \text{Human k to Wall Time}\ut{s} \\ t &= \text{Overall Time}\ut{s} \end{cases} $$ $$ \begin{cases} t_1 &= \frac{L}{v_w} \\ t_2 &= t_1 + \frac{L}{v_w} \\ t_3 &= t_2 + \frac{L}{v_w} \\ \vdots \\ \Delta t &= \frac{L}{v_w} \end{cases} $$ $$ \begin{aligned} n \Delta t &= t \\ n &= \frac{t}{\Delta t} = t\cdot \frac{v_w}{L} \end{aligned} $$ $$ \begin{aligned} \Ans &=\dot D= \dxt{D} = ? \\&= \dt(nd) \\&= \dt(t\cdot \frac{v_w}{L}\cdot d) \\&= \frac{v_wd}{L} \cdot \dxt{t} \\&= \frac{v_wd}{L} \\&= \frac{3.50\ut{m/s}\cdot 0.25\ut{m}}{1.75\ut{m}} \\&= \frac{1}{2}\ut{m/s} \\&= 0.50\ut{m/s} \end{aligned} $$
(b) $$ \Ans = t = D^{-1}(5) =? $$ $$ D(t) = \frac{v_wd}{L}\cdot t $$ $$ D^{-1}(x) = \frac{L}{v_wd} \cdot x $$ $$ \begin{aligned} D^{-1}(5) &= \frac{1.75\ut{m}}{3.50\ut{m/s}\cdot 0.25\ut{m}} \cdot 5 \\ &= 10.0\ut{s} \end{aligned} $$