4-25 할리데이 10판 솔루션 일반물리학

$$\begin{cases} \vec a &= -g\j\\ g &\approx 9.80665\ut{m/s^2}\\ \end{cases}$$ $$\begin{cases} \Delta x &= 77.0\ut{m}\\ \Delta y &= 0\\ \theta &= 12.0\degree\\ \end{cases}$$ $$\begin{aligned} \Delta y &= v_{y0}t+\frac{1}{2}a_yt^2,\\ 0 &= (v_0\sin\theta) t+\frac{1}{2}(-g)t^2\\ 0 &= v_0\sin\theta -\frac{1}{2}gt\\ t &= \frac{2v_0}{g}\sin\theta\\ \end{aligned}$$ $$\begin{aligned} \Delta x &= v_xt,\\ &= (v_0\cos\theta)\(\frac{2v_0}{g}\sin\theta\)\\ &= \frac{v_0^2}{g}\sin(2\theta)\\ \end{aligned}$$ $$\begin{aligned} v_0 &= \sqrt{\frac{\Delta x g}{\sin(2\theta)}}\\ &= \sqrt{\frac{(77.0) (9.80665)}{\sin(2\cdot12.0\degree)}}\\ &\approx43.0872771679\ut{m/s}\\ &\approx43.1\ut{m/s}\\ \end{aligned}$$ $$\begin{aligned} \vec v_0 &\approx 42.1457167839\i+8.95834864871\j\ut{m/s}\\ &\approx 42.1\i+8.96\j\ut{m/s}\\ \end{aligned}$$