+118723 $${\mathtt{18}} = {\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\mathtt{30}}{\mathtt{\,\times\,}}{\mathtt{sin40}}{\mathtt{\,\times\,}}{\mathtt{t}}{\mathtt{\,-\,}}{\mathtt{0.5}}{\mathtt{\,\times\,}}{\mathtt{9.81}}{\mathtt{\,\times\,}}{{\mathtt{t}}}^{{\mathtt{2}}}$$
$${\mathtt{0.5}}{\mathtt{\,\times\,}}{\mathtt{9.81}} = {\frac{{\mathtt{981}}}{{\mathtt{200}}}} = {\mathtt{4.905}}$$
$$\\-4.908t^2+40sin40-16=0\\
\\4.908t^2-40sin40+16=0\\$$$${\mathtt{4.908}}{\mathtt{\,\times\,}}{{\mathtt{t}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{40}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{40}}^\circ\right)}{\mathtt{\,\small\textbf+\,}}{\mathtt{16}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{t}} = {\mathtt{\,-\,}}{\frac{{\mathtt{4}}{\mathtt{\,\times\,}}{{\mathtt{5}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{5}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{2\pi}}}{{sin}}{\left({\frac{{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{\pi}}}{{\mathtt{9}}}}\right)}{\mathtt{\,-\,}}{\mathtt{2}}}}}{{\sqrt{{\mathtt{1\,227}}}}}}\\
{\mathtt{t}} = {\frac{{\mathtt{4}}{\mathtt{\,\times\,}}{{\mathtt{5}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{5}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{2\pi}}}{{sin}}{\left({\frac{{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{\pi}}}{{\mathtt{9}}}}\right)}{\mathtt{\,-\,}}{\mathtt{2}}}}}{{\sqrt{{\mathtt{1\,227}}}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{t}} = -{\mathtt{1.406\: \!665\: \!960\: \!846\: \!221\: \!3}}\\
{\mathtt{t}} = {\mathtt{1.406\: \!665\: \!960\: \!846\: \!221\: \!3}}\\
\end{array} \right\}$$
+118723 $${\mathtt{18}} = {\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\mathtt{30}}{\mathtt{\,\times\,}}{\mathtt{sin40}}{\mathtt{\,\times\,}}{\mathtt{t}}{\mathtt{\,-\,}}{\mathtt{0.5}}{\mathtt{\,\times\,}}{\mathtt{9.81}}{\mathtt{\,\times\,}}{{\mathtt{t}}}^{{\mathtt{2}}}$$
$${\mathtt{0.5}}{\mathtt{\,\times\,}}{\mathtt{9.81}} = {\frac{{\mathtt{981}}}{{\mathtt{200}}}} = {\mathtt{4.905}}$$
$$\\-4.908t^2+40sin40-16=0\\
\\4.908t^2-40sin40+16=0\\$$$${\mathtt{4.908}}{\mathtt{\,\times\,}}{{\mathtt{t}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{40}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{40}}^\circ\right)}{\mathtt{\,\small\textbf+\,}}{\mathtt{16}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{t}} = {\mathtt{\,-\,}}{\frac{{\mathtt{4}}{\mathtt{\,\times\,}}{{\mathtt{5}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{5}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{2\pi}}}{{sin}}{\left({\frac{{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{\pi}}}{{\mathtt{9}}}}\right)}{\mathtt{\,-\,}}{\mathtt{2}}}}}{{\sqrt{{\mathtt{1\,227}}}}}}\\
{\mathtt{t}} = {\frac{{\mathtt{4}}{\mathtt{\,\times\,}}{{\mathtt{5}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{5}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{2\pi}}}{{sin}}{\left({\frac{{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{\pi}}}{{\mathtt{9}}}}\right)}{\mathtt{\,-\,}}{\mathtt{2}}}}}{{\sqrt{{\mathtt{1\,227}}}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{t}} = -{\mathtt{1.406\: \!665\: \!960\: \!846\: \!221\: \!3}}\\
{\mathtt{t}} = {\mathtt{1.406\: \!665\: \!960\: \!846\: \!221\: \!3}}\\
\end{array} \right\}$$
