\documentclass{article}
\usepackage{amsmath}
\usepackage[includehead, includefoot, paperwidth=11in,paperheight=8.5in,margin=0.2in]{geometry}
\usepackage{setspace}
\usepackage{capt-of}
\usepackage{array}
\usepackage{graphics}
\usepackage{tikz}
\usetikzlibrary{positioning, calc, plotmarks, patterns, arrows}
\tikzset{>=stealth}
\usepackage{pgfplots}
\usepackage{booktabs}
\pgfplotsset{compat=1.9}
\setstretch{0.5}
\usepackage{fancyhdr}

\pagestyle{fancy}
\fancyhf{}
\setlength{\headheight}{32pt}
\setlength{\footskip}{18pt}


\renewcommand\footrule{\begin{minipage}{1\textwidth}
\hrule width \hsize height 2pt \kern 1mm \hrule width \hsize
\end{minipage}\par}%

\renewcommand\headrule{
\begin{minipage}{1\textwidth}
\hrule width \hsize \kern 1mm \hrule width \hsize height 2pt
\end{minipage}}%

\lhead{\huge Physics}
\rhead{\huge Projectile Motion}
\rfoot{David, Period 8}

\begin{document}
\begin{tabular}{ >{\centering\arraybackslash} m{6in} >{\centering\arraybackslash} m{3in}}
\begin{tikzpicture}[scale=1, transform shape] %angular projection
\begin{axis}[
width=\linewidth, %set bigger width
height={3in},
xmin=0,xmax=11.5,
ymin=0,ymax=4,
xlabel=$x$,
ylabel=$y$,
axis x line = bottom,
axis y line = left,
axis line style={->},
%axis on top,
ticks = none,clip=false,
]

\tikzset{every mark/.append style={fill=white}}
%variable definitions
\def\g{-9.8} %gravity
\def\v{10} %velocity
\def\ang{51} %angle
\def\s{0.18}
\pgfmathsetmacro{\t}{0}

%flight path
\addplot[
dashed,
domain=0:10,
samples=100,]
{{\g*(x^2)/(2*\v^2*cos(\ang)^2)+x*tan(\ang)}}
node[midway,above]{$\vec{V}_y=0$};

%vector at start
\coordinate (A) at (axis cs: {\v*cos(\ang)*\t}, {\v*\t*sin(\ang)+0.5*\g*(\t^2)});
\coordinate (B) at (axis cs: {\v*cos(\ang)*\t+\s*\v*cos(\ang)}, {\v*\t*sin(\ang)+0.5*\g*\t^2+\s*(\v*sin(\ang)+\g*\t)});
\draw[very thick,->](A)--(B)
node[midway,sloped,above]{$\vec{V}$};
\draw[densely dashed,very thick,->](A)--(B|-A)
node[midway,below]{$\vec{V}_x$};
\draw[densely dashed,very thick,->](A)--(B-|A)
node[midway,left]{$\vec{V}_y$};

\path plot[mark=*] coordinates {(A)};

%dashed box around start vector
\draw[dashed](B-|A)--(B);
\draw[dashed](B|-A)--(B);

%vector at end
\pgfmathsetmacro{\a}{{-1*(2/\g)*\v*sin(\ang)}}
\coordinate (E) at (axis cs:{\v*cos(\ang)*\a},{\v*\a*sin(\ang)+0.5*\g*(\a^2)}){};
\coordinate (F) at (axis cs:{\v*cos(\ang)*\a+\s*\v*cos(\ang))}, {\v*\a*sin(\ang)+0.5*\g*\a^2+\s*(\v*sin(\ang)+\g*\a)});
\draw[very thick,->](E)--(F)
node[midway,sloped,above]{$\vec{V}$};
\draw[densely dashed,very thick,->](E)--(F |- E)
node[midway,above]{$\vec{V}_x$};
\draw[densely dashed,very thick,->](E)--(F-| E)
node[midway,left]{$\vec{V}_y$};

\path plot[mark=*] coordinates {(E)};

%vector 1/2 up
\pgfmathsetmacro{\b}{{(-1*(2/\g)*\v*sin(\ang))/4}}
\coordinate (H) at (axis cs:{\v*cos(\ang)*\b},{\v*\b*sin(\ang)+0.5*\g*(\b^2)});
\coordinate (I) at (axis cs: {\v*cos(\ang)*\b+\s*\v*cos(\ang)},{\v*\b*sin(\ang)+0.5*\g*\b^2+\s*(\v*sin(\ang)+\g*\b)});
\draw[very thick,->](H)--(I)
node[midway,sloped,above]{$\vec{V}$};
\draw[densely dashed,very thick,->](H)--(I-|H)
node[midway,left]{$\vec{V}_y$};
\draw[densely dashed,very thick,->](H)--(I|-H)
node[midway,below]{$\vec{V}_x$};

\path plot[mark=*] coordinates {(H)};

%vector halfway
\pgfmathsetmacro{\c}{{(-1*(2/\g)*\v*sin(\ang))/2}}
\coordinate (L) at (axis cs:{\v*cos(\ang)*\c},{\v*\c*sin(\ang)+0.5*\g*(\c^2)});
\coordinate (M) at (axis cs:{\v*cos(\ang)*\c+\s*\v*cos(\ang))},{\v*\c*sin(\ang)+0.5*\g*\c^2+\s*(\v*sin(\ang)+\g*\c)});
\draw[very thick,->](L)--(M)
node[midway,sloped,below]{$\vec{V}$};


%T2 line; halfway up flight path
\draw[loosely dashed] (L) -- (axis cs:{\v*cos(\ang)*\c},0)
node[midway,right,font=\small] {$\dfrac{t_\text{total}}{2}$};


\path plot[mark=*] coordinates {(L)};

%vector 1/2 down
\pgfmathsetmacro{\d}{{(-1*(2/\g)*\v*sin(\ang))*0.75}}
\coordinate (P) at (axis cs:{\v*cos(\ang)*\d},{\v*\d*sin(\ang)+0.5*\g*(\d^2)});
\coordinate (Q) at (axis cs:{(\v*cos(\ang)*\d+\s*\v*cos(\ang))},{\v*\d*sin(\ang)+0.5*\g*\d^2+\s*(\v*sin(\ang)+\g*\d)});
\draw[very thick,->](P)--(Q)
node[midway,sloped,above]{$\vec{V}$};
\draw[densely dashed,very thick,->](P)--(Q|-P)
node[midway,above]{$\vec{V}_x$};
\draw[densely dashed,very thick,->](P)--(Q-|P)
node[midway,left]{$\vec{V}_y$};

\path plot[mark=*] coordinates {(P)};

%start vector angle label
\node[circle,minimum size=25pt] at (A) (circ) {};
\node[right] at (circ.35) {$\theta$};
\path[clip] (A) -- (B) -- (B|-A) -- cycle;
\node[circle,draw,minimum size=25pt] at (A) (circ) {};
\end{axis}
\end{tikzpicture} &
\captionof{table}{Angular Projection}
\resizebox{\linewidth}{!}{%
\begin{tabular}{@{}cc@{}}
\toprule
\textbf{Horizontal Motion} & \textbf{Vertical Motion} \\ \midrule
$V_{X_i}=V \cos \theta$ & $V_{y_i}=V \sin \theta$ \\
$X=V_{X_i}t_\text{total}$ & $t_{y_\text{max}}=\dfrac{V \sin \theta}{g}$ \\
$t_\text{total}=\dfrac{2V \sin \theta}{g}$ & $V_y=V_{y_i}-gt$ \\
$X=\dfrac{V^2 \sin 2 \theta}{g}$ & $y=V_{y_i}t-\dfrac{1}{2}gt^2$ \\
 & ${V_y}^2={V_{y_i}}^2-2gy$ \\
 & $y_\text{max}=\dfrac{(V \sin \theta)^2}{2g}$ \\ \bottomrule
\end{tabular}%
} \\
\begin{tikzpicture}[scale=1, transform shape]  %horizontal projection
%variable definitions
\def\g{-9.8} %gravity
\def\v{10} %velocity
\def\ang{51} %angle
\def\s{0.125}
\pgfmathsetmacro{\c}{{(-1*(2/\g)*\v*sin(\ang))/2}}
\pgfmathsetmacro{\a}{{(-1*(2/\g)*\v*sin(\ang))*.9}}

\begin{axis}[
width=.7\linewidth, %set bigger width
height=4in,
xmin={{\v*cos(\ang)*\c}},xmax=10, %{\v*cos(\ang)*\a+\s*\v*cos(\ang)}
ymin=0,ymax={\v*\c*sin(\ang)+0.5*\g*(\c^2)},
xlabel=$X$,
ylabel=$y$,
axis x line = bottom,
clip bounding box=upper bound,
axis y line = left,
y axis line style={<-},
x axis line style={<->},
ticks = none,clip=false,
]

\tikzset{every mark/.append style={fill=white}}

%flight path
\addplot[
dashed,
domain={\v*cos(\ang)*\c}:10,
samples=100,]
{{\g*(x^2)/(2*\v^2*cos(\ang)^2)+x*tan(\ang)}};

%vector at end
\pgfmathsetmacro{\a}{{(-1*(2/\g)*\v*sin(\ang))*.9}}
\coordinate (E) at (axis cs:{\v*cos(\ang)*\a},{\v*\a*sin(\ang)+0.5*\g*(\a^2)}){};
\coordinate (F) at (axis cs:{\v*cos(\ang)*\a+\s*\v*cos(\ang))}, {\v*\a*sin(\ang)+0.5*\g*\a^2+\s*(\v*sin(\ang)+\g*\a)});
\draw[very thick,->](E)--(F)
node[midway,sloped,above]{$\vec{V}$};
\draw[densely dashed,very thick,->](E)--(F |- E)
node[midway,above]{$\vec{V}_x$};
\draw[densely dashed,very thick,->](E)--(F-| E)
node[midway,left]{$\vec{V}_y$};

\path plot[mark=*] coordinates {(E)};

%vector at start
\pgfmathsetmacro{\c}{{(-1*(2/\g)*\v*sin(\ang))/2}}
\coordinate (L) at (axis cs:{\v*cos(\ang)*\c},{\v*\c*sin(\ang)+0.5*\g*(\c^2)});
\coordinate (M) at (axis cs:{\v*cos(\ang)*\c+\s*\v*cos(\ang))},{\v*\c*sin(\ang)+0.5*\g*\c^2+\s*(\v*sin(\ang)+\g*\c)});
\draw[very thick,->](L)--(M)
node[midway,sloped,above]{$\vec{V}$};

\path plot[mark=*] coordinates {(L)};

%vector 1/2 down
\pgfmathsetmacro{\d}{{(-1*(2/\g)*\v*sin(\ang))*0.6}}
\coordinate (P) at (axis cs:{\v*cos(\ang)*\d},{\v*\d*sin(\ang)+0.5*\g*(\d^2)});
\coordinate (Q) at (axis cs:{(\v*cos(\ang)*\d+\s*\v*cos(\ang))},{\v*\d*sin(\ang)+0.5*\g*\d^2+\s*(\v*sin(\ang)+\g*\d)});
\draw[very thick,->](P)--(Q)
%node[midway,sloped,above]{$\vec{V}$}
;
\draw[densely dashed,very thick,->](P)--(Q|-P)
node[midway,above]{$\vec{V}_x$};
\draw[densely dashed,very thick,->](P)--(Q-|P)
node[midway,left]{$\vec{V}_y$};

\path plot[mark=*] coordinates {(P)};

%vector 3/4 down
\pgfmathsetmacro{\f}{{(-1*(2/\g)*\v*sin(\ang))*0.7}}
\coordinate (R) at (axis cs:{\v*cos(\ang)*\f},{\v*\f*sin(\ang)+0.5*\g*(\f^2)});
\coordinate (S) at (axis cs:{(\v*cos(\ang)*\f+\s*\v*cos(\ang))},{\v*\f*sin(\ang)+0.5*\g*\f^2+\s*(\v*sin(\ang)+\g*\f)});
\draw[very thick,->](R)--(S)
node[midway,above,sloped]{$\vec{V}$};
\draw[densely dashed,very thick,->](R)--(S|-R)
node[midway,above]{$\vec{V}_x$};
\draw[densely dashed,very thick,->](R)--(S-|R)
node[midway,left]{$\vec{V}_y$};

\path plot[mark=*] coordinates {(R)};

%vector 1/4 down
\pgfmathsetmacro{\e}{{(-1*(2/\g)*\v*sin(\ang))*0.8}}
\coordinate (T) at (axis cs:{\v*cos(\ang)*\e},{\v*\e*sin(\ang)+0.5*\g*(\e^2)});
\coordinate (U) at (axis cs:{(\v*cos(\ang)*\e+\s*\v*cos(\ang))},{\v*\e*sin(\ang)+0.5*\g*\e^2+\s*(\v*sin(\ang)+\g*\e)});
\draw[very thick,->](T)--(U)
node[midway,sloped,above]{$\vec{V}$};
\draw[densely dashed,very thick,->](T)--(U|-T)
node[midway,above]{$\vec{V}_x$};
\draw[densely dashed,very thick,->](T)--(U-|T)
node[midway,left]{$\vec{V}_y$};

\path plot[mark=*] coordinates {(T)};

%free fall comparison plots
\pgfmathsetmacro{\z}{{(\v*cos(\ang)*\c+\s*\v*cos(\ang))*0.925}}

\draw[very thick,->] (axis cs:\z,{\v*\e*sin(\ang)+0.5*\g*(\e^2)}) -- (axis cs:\z,{\v*\e*sin(\ang)+0.5*\g*\e^2+\s*(\v*sin(\ang)+\g*\e)});
\draw[very thick,->] (axis cs:\z,{\v*\f*sin(\ang)+0.5*\g*(\f^2)}) -- (axis cs:\z,{\v*\f*sin(\ang)+0.5*\g*\f^2+\s*(\v*sin(\ang)+\g*\f)});
\draw[very thick,->] (axis cs:\z,{\v*\d*sin(\ang)+0.5*\g*(\d^2)}) -- (axis cs:\z,{\v*\d*sin(\ang)+0.5*\g*\d^2+\s*(\v*sin(\ang)+\g*\d)});
\draw[very thick,->] (axis cs:\z,{\v*\a*sin(\ang)+0.5*\g*(\a^2)}) -- (axis cs:\z,{\v*\a*sin(\ang)+0.5*\g*\a^2+\s*(\v*sin(\ang)+\g*\a)})
node[midway,right]{Vertical fall}
;
\path plot[mark=*] coordinates {(axis cs:\z,{\v*\e*sin(\ang)+0.5*\g*(\e^2)})};
\path plot[mark=*] coordinates {(axis cs:\z,{\v*\f*sin(\ang)+0.5*\g*(\f^2)})};
\path plot[mark=*] coordinates {(axis cs:\z,{\v*\d*sin(\ang)+0.5*\g*(\d^2)})};
\path plot[mark=*] coordinates {(axis cs:\z,{\v*\a*sin(\ang)+0.5*\g*(\a^2)})};


\end{axis}
\end{tikzpicture} &
\captionof{table}{Horizontal Projection} % title of Table
\resizebox{\linewidth}{!}{%
\begin{tabular}{@{}cc@{}}
\toprule
\textbf{Horizontal Motion} & \textbf{Vertical Motion} \\ \midrule
$V_x=V_{X_i}$ & $V_y=gt$ \\
$X=V_x t$ & $y=\frac{1}{2}gt^2$ \\
 & ${V_y}^2=2g(\Delta y)$ \\ \bottomrule
\end{tabular}%
}
\end{tabular}
\end{document}