1-19 할리데이 10판 솔루션 일반물리학

 

$$\begin{aligned} \omega &= \frac{2\pi\ut{rad}}{1\ut{days}} \\&= \frac{2\pi\ut{rad}}{1\ut{days}}\cdot \frac{1\ut{days}}{24\ut{h}}\cdot \frac{1\ut{h}}{3600\ut{s}} \\&=\frac{\pi }{43200}\ut{rad/s} \end{aligned}$$ $$\begin{cases} H &= 1.70\ut{m} \\ t &= 11.1\ut{s} \\ \omega &= \frac{\pi }{43200}\ut{rad/s} \end{cases}$$ $$\begin{cases} \theta &= \omega t \\ \cos \theta &= \frac{R}{R+H} \end{cases}$$ $$\begin{aligned} \frac{R}{R+H} &= \cos(\omega t) \\ \frac{R+H}{R} &= \sec(\omega t) \\ 1+\frac{H}{R} &= \sec(\omega t) \\ \frac{H}{R} &= \sec(\omega t)-1 \\ R &= \frac{H}{\sec(\omega t)-1} \\ &= \frac{1.70\ut{m}}{\sec\left(\frac{\pi }{43200}\ut{rad/s} \cdot 11.1\ut{s}\right)-1} \\ &\approx 5.217958129139526\times 10^6\ut{m} \\ &\approx 5.22\times 10^6\ut{m} = 5220\ut{km} \end{aligned}$$