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+FJ(\()p FD(x)1430 4445 y FG(1)1468 4433 y FJ(;)14 b FD(y)1546 4445 y FG(1)1583 4433 y FJ(\))p FW(,)34 b(il)91 4533 y(faut)24 b(partir)f(de)h(l'\351quation)f(de)h(la)g(parab)r(ole)e (appli-)91 4632 y(qu\351e)28 b(au)f(p)r(oin)n(t)h(C)f(:)119 diff --git a/MecaniqueDim/MecaniqueDim.tex b/MecaniqueDim/MecaniqueDim.tex index aaf245d..1a369c6 100644 --- a/MecaniqueDim/MecaniqueDim.tex +++ b/MecaniqueDim/MecaniqueDim.tex @@ -195,11 +195,11 @@ et on remplace dans la seconde~: où on a utilisé la définition de la tangente~: \[\tan(\beta)=\sin(\beta)/\cos(\beta)\] En mettant en évidence \(T_1\) et le déplaçant à droite de l'équation, on a~: -\[F-P=T_1\cdot (\sin(\alpha)+\sin(\beta))\] +\[F-P=T_1\cdot (\sin(\alpha)+\cos(\alpha)\cdot\tan(\beta))\] et donc finalement avec \(P=m\cdot g\)~: -\[T_1=\frac{F-m\cdot g}{\sin(\alpha)+\sin(\beta)}\] +\[T_1=\frac{F-m\cdot g}{\sin(\alpha)+\cos(\alpha)\cdot\tan(\beta)}\] et pour \(T_2\)~: -\[T_2=\frac{(F-m\cdot g)\cdot \cos(\alpha)}{\cos(\beta)\cdot (\sin(\alpha)+\sin(\beta))}\] +\[T_2=\frac{(F-m\cdot g)\cdot \cos(\alpha)}{\cos(\beta)\cdot (\sin(\alpha)+\cos(\alpha)\cdot\tan(\beta))}\] \subsection{Plan incliné} \begin{figure}[t] @@ -359,7 +359,7 @@ Car, \(2\cdot \sin(\alpha)\cos(\alpha)=\sin(2\cdot \alpha)\).\\ Une conséquence de ce résultat est qu'on peut déterminer l'angle sous lequel on doit tirer pour que le tir une porté L~: \begin{align*} L&=\frac{v_o^2}{g}\cdot \sin(2\cdot \alpha)\;\Rightarrow\;\sin(2\cdot \alpha)=\frac{g\cdot L}{v_o^2}\\ -&\Rightarrow\;\alpha = \arcsin(\frac{g\cdot L}{v_o^2}) +&\Rightarrow\;\alpha = \arcsin(\frac{g\cdot L}{v_o^2})/2 \end{align*} \item Pour déterminer l'angle nécessaire pour atteindre le point C de coordonnée \((x_1;y_1)\), il faut partir de l'équation de la parabole appliquée au point C~: \[y_1=-\frac{1}{2}\cdot g\cdot\left(\frac{x_1}{v_o}\right)^2\cdot \frac{1}{\cos^2(\alpha)}+x_1\cdot \tan(\alpha)\]