4-31 할리데이 10판 솔루션 일반물리학

$$\begin{cases} \vec r_Q &= (32,3.5)\ut{m}\\ \vec r_P &= (0,1.0)\ut{m}\\ \vec v_0 &= (18\ut{m/s},40\degree)\\ \vec a &=-g\j\\ g &\approx 9.80665\ut{m/s^2}\\ \end{cases}$$ $$\title{Over Q Point Possible?}$$ $$v_0 = 18\cos40\degree\i+18\sin40\degree\j,$$ $$\begin{aligned} t &= \frac{\Delta x}{v_x}\\ &= \frac{32}{18\cos40\degree}\\ &= \frac{16}{9} \sec40\degree\\ \end{aligned}$$ $$\begin{aligned} \Delta y &= v_{y0}t+\frac{1}{2}a_yt^2,\\ &= \(18\sin40\degree\) \(\frac{16}{9} \sec40\degree\)-\frac{1}{2}g\(\frac{16}{9} \sec40\degree\)^2\\ &=32 \tan 40\degree-\frac{128}{81} g \sec ^2 40\degree\\ &\approx0.443055522227\ut{m} < 2.5\ut{m} \end{aligned}$$ $$\title{Over Q Point Impossible}$$