10판/2. 직선운동

2-9 할리데이 10판 솔루션 일반물리학

짱세디럭스 2019. 7. 22. 19:36

(L1=1[km]L_1=1\ut{km} 로 추정함.) {S=1[km]t1=2[min]+27.95[s]=147.95[s]t2=2[min]+28.15[s]=148.15[s]L2=L1+ΔLv1>v2 \begin{cases} S &= 1\ut{km} \\ t_1 &= 2\ut{min}+27.95\ut{s} = 147.95\ut{s} \\ t_2 &= 2\ut{min}+28.15\ut{s} = 148.15\ut{s} \\ L_2 &= L_1 + \Delta L \\ v_1 &> v_2 \end{cases} v1>v2L1t1>L2t2L1t1>L1+ΔLt2L1t1>L1t2+ΔLt2ΔLt2<L1t1L1t2ΔL<t2(L1t1L1t2)ΔL<t2L1(1t11t2)ΔL<L1t2t2t1t1t2ΔL<L1t2t1t1ΔL<L1(t2t11)ΔL<1[km](148.15[s]147.95[s]1)1000[m]1[km]ΔL<40002959[m]1.352[m] \begin{aligned} v_1 &> v_2 \\ \frac{L_1}{t_1} &> \frac{L_2}{t_2} \\ \frac{L_1}{t_1} &> \frac{L_1 + \Delta L}{t_2} \\ \frac{L_1}{t_1} &> \frac{L_1}{t_2}+\frac{\Delta L}{t_2} \\ \\ \frac{\Delta L}{t_2} &< \frac{L_1}{t_1} - \frac{L_1}{t_2} \\ \Delta L &< t_2\(\frac{L_1}{t_1} - \frac{L_1}{t_2}\) \\ \Delta L &< t_2L_1\(\frac{1}{t_1} - \frac{1}{t_2}\) \\ \Delta L &< L_1t_2\frac{t_2-t_1}{t_1t_2} \\ \Delta L &< L_1\frac{t_2-t_1}{t_1} \\ \Delta L &< L_1\(\frac{t_2}{t_1}-1\) \\ \\ \Delta L &< 1\ut{km}\cdot \(\frac{148.15\ut{s}}{147.95\ut{s}}-1\)\cdot \frac{1000\ut{m}}{1\ut{km}} \\ \Delta L &< \frac{4000}{2959}\ut{m} \approx 1.352\ut{m} \end{aligned}