10판/3. 벡터

3-18 할리데이 10판 솔루션 일반물리학

짱세디럭스 2019. 8. 7. 19:44

{A+B=CA:(12.0,40)C:(16.0,200)\begin{cases} \vec A + \vec B= \vec C\\ \vec A:(12.0,40^\circ)\\ \vec C:(16.0,200^\circ)\\ \end{cases} A=(12cos40)i^+(12sin40)j^\vec A = (12\cos40^\circ)\hat i + (12\sin40^\circ)\hat j C=(16cos200)i^+(16sin200)j^\vec C = (16\cos200^\circ)\hat i + (16\sin200^\circ)\hat j B=CA=(16cos20012cos40)i^+(16sin20012sin40)j^ \begin{aligned} \vec B &= \vec C - \vec A\\ &=(16\cos200^\circ-12\cos40^\circ)\hat i + (16\sin200^\circ-12\sin40^\circ)\hat j\\ \end{aligned}
(a)B=? B=(16cos20012cos40)2+(16sin20012sin40)2=424cos20+2527.6[m] \begin{aligned} B&=\sqrt{(16\cos200^\circ-12\cos40^\circ)^2+(16\sin200^\circ-12\sin40^\circ)^2}\\ &=4 \sqrt{24 \cos20^{\circ}+25}\\ &\approx 27.6\ut{m}\\ \end{aligned}
(b)θB=?\theta_B=? θB=tan1(16sin20012sin4016cos20012cos40)2.64[rad] \begin{aligned} \theta_B&=\tan^{-1}\(\frac{16\sin200^\circ-12\sin40^\circ}{16\cos200^\circ-12\cos40^\circ}\)\\ &\approx -2.64\ut{rad} \end{aligned}