Example: Projectile

Published 2009-11-25 | Author: Jon Engel

I made it for an introductory physics class to explain a common demonstration: if you aim a gun at a target held in the air, and fire the instant the target is dropped, you always hit the target, no matter how fast your bullet goes. There are a lot of numbers hard coded in, but it’s not hard to alter the second example so that the initial velocity of the bullet is different. You just change v0 and the number of frames (and the arrow representing v0). I’m sure it can be made much more elegant.

Download as: [PDF] [TEX]  •  [Open in Overleaf]

Projectile

Do you have a question regarding this example, TikZ or LaTeX in general? Just ask in the LaTeX Forum.
Oder frag auf Deutsch auf TeXwelt.de. En français: TeXnique.fr.

% Projectile
% Author: Jon Engel
\documentclass{beamer}
\usepackage{tikz}
\usetikzlibrary{decorations.pathreplacing}
\usepackage{animate}
\usepackage{ifthen}
\setbeamertemplate{navigation symbols}{}

\begin{document}

\begin{frame}
\begin{columns}\begin{column}{6cm}
\begin{animateinline}[poster=first,controls]{8}%
   \multiframe{21}{rt=0+.1,icount=1+1,rvo=3+0}{%
%rt is the time and rvo the initial velocity, in units in which g=2.
   \begin{tikzpicture}[scale=.75]
      \clip (-.3,-.3) rectangle (9,7);
      \draw[ultra thick,-latex] (0,.5) -- node[above left]{$\vec{v}_0$} (1.5,2);
      \node[draw=gray,name=tar0,text=gray,dashed,outer sep=6pt] at (6,6)  
                                                                      {target};
      \node[draw=red,fill=white,name=tar,text=red,outer sep=6pt] at 
                                                        (6,6-\rt*\rt) {target}; 
      \draw[blue] (0,0) circle (3pt);
      \ifthenelse{\icount > 1}% 
         {\draw[ultra thick,blue,->] (0,0) -- (\rvo*\rt,\rvo*\rt);
          \foreach \x in {.0,.1,...,\rt} \draw[blue] 
                                    (\rvo*\x,\rvo*\x-\x*\x) circle (3pt);}{}
      \ifthenelse{\icount > 5}%
         {\draw[ultra thick,blue,->,shorten < =5pt] 
                      (\rvo*\rt,\rvo*\rt) -- (\rvo*\rt,\rvo*\rt-\rt*\rt);}{}
      \ifthenelse{\icount > 7}
         {\draw[decorate,decoration={brace,amplitude=2mm},red] 
                                       (tar0.east) -- (tar.east);}{}
      \ifthenelse{\icount > 14}
         {\node[text=blue] at (4,4.8) {$\vec{v}_0 t$};
          \node[text=blue] at (\rvo*\rt-.8,1.5+\rt) {$-\frac{gt^2}{2}\hat{j}$};
          \node[text=red] at (7.9,6-.5*\rt*\rt) {$\frac{gt^2}{2}$};
          \node[fill=yellow!20] at (2,6.5) 
                          {$\vec{r}=\vec{v}_0 t-\frac{gt^2}{2}\hat{j}$};}{}
   \end{tikzpicture}%
   }
\end{animateinline}
%
\end{column}\begin{column}{6cm}
\begin{animateinline}[poster=first,controls]{8}%
   \multiframe{16}{rt=0+.1,icount=1+1,rvo=4+0}{%
   \begin{tikzpicture}[scale=.75]
      \clip (-.3,-.3) rectangle (9,7);
      \draw[ultra thick,-latex] (0,.5) -- node[above left]{$\vec{v}_0$} (2,2.5);
      \node[draw=gray,text=gray,dashed,outer sep=6pt] at (6,6) {target};
          \node[draw=red,fill=white,text=red,outer sep=6pt] at 
                                                        (6,6-\rt*\rt) {target}; 
      \draw[blue] (0,0) circle (3pt);
      \ifthenelse{\icount > 1}%
         {\draw[ultra thick,blue,->] (0,0) -- (\rvo*\rt,\rvo*\rt);
          \foreach \x in {.0,.1,...,\rt} \draw[blue] 
                                   (\rvo*\x,\rvo*\x-\x*\x) circle (3pt);}{}
      \ifthenelse{\icount > 5}%
         {\draw[ultra thick,blue,->,shorten < =5pt] 
                      (\rvo*\rt,\rvo*\rt) -- (\rvo*\rt,\rvo*\rt-\rt*\rt);}{}
   \end{tikzpicture}%
   }%
\end{animateinline}
\end{column}\end{columns}
\end{frame} 

\end{document}

Comments

  • #1 jigal, November 25, 2009 at 9:45 p.m.

    Beautiful! Never known you can make this with latex

Adding comments is currently not enabled.

Features
Tags
Scientific and technical areas

Cookbook

LaTeX Beginners Guide

Limited discount 50%
coupon code tDRet6Y

Creative Commons License