11판/4. 2차원 운동과 3차원 운동

4-3 할리데이 11판 솔루션 일반물리학

짱세디럭스 2024. 1. 26. 15:25
{vA0=520[m/s],θA=14.0°vB0=630[m/s],θB=16.0°vC0=750[m/s],θC=18.0°vD0=870[m/s],θD=20.0°vE0=1000[m/s],θE=22.0°g=9.80665[m/s2] \begin{cases} v_{A0}=520\ut{m/s},& \theta_A=14.0\degree\\ v_{B0}=630\ut{m/s},& \theta_B=16.0\degree\\ v_{C0}=750\ut{m/s},& \theta_C=18.0\degree\\ v_{D0}=870\ut{m/s},& \theta_D=20.0\degree\\ v_{E0}=1000\ut{m/s},& \theta_E=22.0\degree\\ g=9.80665\ut{m/s^2} \end{cases} Δx=vxt=v0tcosθ \begin{aligned} \Delta x &= v_xt\\ &=v_0t\cos\theta \end{aligned} Δy=vy0t+12(g)t2=v0tsinθ12gt2 \begin{aligned} \Delta y &=v_{y0}t+\frac{1}{2}(-g)t^2\\ &=v_0t\sin\theta-\frac{1}{2}gt^2\\ \end{aligned} (a)\ab{a} Rt=20=(v0tcosθ,v0tsinθ12gt2)=(20v0cosθ,20v0sinθ200g) \begin{aligned} R_{t=20}&=\(v_0t\cos\theta,v_0t\sin\theta-\frac{1}{2}gt^2\)\\ &=\(20v_0\cos\theta,20v_0\sin\theta-200g\)\\ \end{aligned} {A:(20vA0cosθA,20vA0sinθA200g)B:(20vB0cosθB,20vB0sinθB200g)C:(20vC0cosθC,20vC0sinθC200g)D:(20vD0cosθD,20vD0sinθD200g)E:(20vE0cosθE,20vE0sinθE200g) \begin{cases} A:\(20v_{A0}\cos\theta_A,20v_{A0}\sin\theta_A-200g\)\\ B:\(20v_{B0}\cos\theta_B,20v_{B0}\sin\theta_B-200g\)\\ C:\(20v_{C0}\cos\theta_C,20v_{C0}\sin\theta_C-200g\)\\ D:\(20v_{D0}\cos\theta_D,20v_{D0}\sin\theta_D-200g\)\\ E:\(20v_{E0}\cos\theta_E,20v_{E0}\sin\theta_E-200g\)\\ \end{cases} ={A:(20520cos14°,20520sin14°200g)B:(20630cos16°,20630sin16°200g)C:(20750cos18°,20750sin18°200g)D:(20870cos20°,20870sin20°200g)E:(201000cos22°,201000sin22°200g) =\begin{cases} A:\(20\cdot520\cdot \cos14\degree,20\cdot520\cdot \sin14\degree-200g\)\\ B:\(20\cdot630\cdot \cos16\degree,20\cdot630\cdot \sin16\degree-200g\)\\ C:\(20\cdot750\cdot \cos18\degree,20\cdot750\cdot \sin18\degree-200g\)\\ D:\(20\cdot870\cdot \cos20\degree,20\cdot870\cdot \sin20\degree-200g\)\\ E:\(20\cdot1000\cdot \cos22\degree,20\cdot1000\cdot \sin22\degree-200g\)\\ \end{cases} {A:(10091.07555327036,554.6577142365445)[m]B:(12111.89736882282,1511.70068329419)[m]C:(14265.8477444273,2673.924915624212)[m]D:(16350.65160167481,3989.820493866636)[m]E:(18543.67709133575,5530.80186831824)[m] \approx \begin{cases} A:\(10091.07555327036, 554.6577142365445\)\ut{m}\\ B:\(12111.89736882282, 1511.70068329419\)\ut{m}\\ C:\(14265.8477444273, 2673.924915624212\)\ut{m}\\ D:\(16350.65160167481, 3989.820493866636\)\ut{m}\\ E:\(18543.67709133575, 5530.80186831824\)\ut{m}\\ \end{cases} {A:(10.1,0.555)[km]B:(12.1,1.51)[km]C:(14.3,2.67)[km]D:(16.4,3.99)[km]E:(18.5,5.53)[km] \approx \begin{cases} A:\(10.1, 0.555\)\ut{km}\\ B:\(12.1, 1.51\)\ut{km}\\ C:\(14.3, 2.67\)\ut{km}\\ D:\(16.4, 3.99\)\ut{km}\\ E:\(18.5, 5.53\)\ut{km}\\ \end{cases} (b)\ab{b} {x=v0tcosθy=v0tsinθ12gt2 \begin{cases} x &=v_0t\cos\theta\\ y &=v_0t\sin\theta-\frac{1}{2}gt^2\\ \end{cases} y=(xcosθ)sinθ12g(xv0cosθ)2=(tanθ)x(g2v02sec2θ)x2 \begin{aligned} y&=\(\frac{x}{\cos\theta}\)\sin\theta-\frac{1}{2}g\(\frac{x}{v_0\cos\theta}\)^2\\ &=(\tan\theta)x-\(\frac{g}{2{v_0}^2}\sec ^2\theta\)x^2 \end{aligned}