Projectile motion: change an old code and make it more beautiful

Given this image,

where a golf player throws a ball with a angle of 54.0° above horizontal and a speed v₀=13.5 m/s. Looking this excellent old answer Sketching a graph mapping projectile motion using LaTeX of the user @Mark Wibrow

with the complete code:

\documentclass[tikz,border=5]{standalone}
\usepackage[prefix=]{xcolor-material}
\begin{document}
\begin{tikzpicture}[x=(330:1cm),y=(30:1cm),z=(90:1cm)]
\fill [LightGreen] (-1,-1,0) -- (-.5,1,0) -- (11,2,0) -- (11,-2,0) -- cycle;
\draw [Brown, thick, line cap=round] (10,0,0) -- (10,0,1);
\fill [Red] (10,0,1) -- (9.8,0,0.9) -- (10,0,0.8) -- cycle;
\fill [Yellow, shift={(7,0,0)}]
plot [domain=0:340, samples=20, smooth cycle, variable=\t]
(\t:rnd/16+0.25 and rnd/8+0.75);
\foreach \a [evaluate={\v=70; \T=\v*sin(\a)/9.807*2;}] in {10, 20, ..., 80} {
\draw [x=(330:0.5pt), z=(90:0.5pt), Black, dashed]
plot [smooth, domain=0:\T, samples=50, variable=\t]
(\v*\t*cos \a, 0, -9.807/2*\t^2+\v*\t*sin \a +0.1016) coordinate (end);
}
\end{tikzpicture}
\end{document}


Starting from the equation of the common trajectory

y=(tan α)x-[1/(2gv₀²cos²α)]x²


is it possible

• to add the x-axis and the y-axis with the tick marks (and the labels)?
• to have the balls of golf very closer near the hight height with below the dashed black line (or continue line) of the trajectory, like the start image?

EDIT:

I have changed a bit the code of the vanish OP....

\documentclass[tikz,border=5]{standalone}
\usepackage[prefix=]{xcolor-material}
\begin{document}
\begin{tikzpicture}[x=(330:1cm),y=(30:1cm),z=(90:1cm),
declare function={v=70;% <- velocity (input)
alpha=30;% <- angle (input)
h=2*v*sin(alpha)/9.807;}]
\fill [LightGreen] (-1,-1,0) -- (-.5,1,0) -- (11,2,0) -- (11,-2,0) -- cycle;
\draw [Brown, thick, line cap=round] (10,0,0) -- (10,0,1);
\fill [Red] (10,0,1) -- (9.8,0,0.9) -- (10,0,0.8) -- cycle;
\fill [Yellow, shift={(7,0,0)}]
plot [domain=0:320, samples=40, smooth cycle, variable=\t]
(\t:rnd/16+0.25 and rnd/8+0.75);
\draw [x=(330:0.5pt), z=(90:0.5pt), White, dash pattern=on 0.1pt off 4pt, double, double distance=1pt, line cap=round]
plot [smooth, domain=0:h, samples=50, variable=\t]
({v*\t*cos(alpha)}, 0,{-9.807/2*\t*\t+v*\t*sin(alpha)+0.1016})
coordinate (end);
\end{tikzpicture}
\end{document}


but I am not able to put the trajectory, the distance between the balls, and the axis with the labels that it is appear like a 3D-drawing.

• *I give to all users always always thank you very much for your precious contributes for me. Nov 10 '20 at 15:38

Two major changes:

• lines that draw the two axes as well as the origin and
• some <mark options> used in \draw plot[..., <mark options>] that draw the (equally x-spaced) balls of golf.
\documentclass{article}
\usepackage{tikz}
\usepackage[prefix=]{xcolor-material}

\begin{document}
\begin{tikzpicture}[x=(330:1cm),y=(30:1cm),z=(90:1cm)]
% green ground
\fill [LightGreen] (-1,-1,0) -- (-.5,1,0) -- (11,2,0) -- (11,-2,0) -- cycle;
% black hole
% red flag
\draw[Brown, thick, line cap=round] (10,0,0) -- (10,0,1);
\fill[Red] (10,0,1) -- (9.8,0,0.9) -- (10,0,0.8) -- cycle;
% yellow sand hill
\fill[Yellow, shift={(7,0,0)}]
plot [domain=0:340, samples=20, smooth cycle, variable=\t]
(\t:rnd/16+0.25 and rnd/8+0.75);

% origin
\node[below left] {$O$};
% x-axis
\draw (0, 0) -- (10, 0)
node[midway, yshift=-.8cm, rotate=330] {Distance, x (m)};
\draw foreach \i in {2,4,6,8}
{ (\i, 0) node[below, rotate=330] {\i} -- ++(0, .15) };
% y-axis
\draw (0, 0, 0) -- (0, 0, 5)
node[pos=.8, xshift=-.8cm, rotate=90] {Height, y(m)};
\draw foreach \i in {2,4}
{ (0, 0, \i) node[left] {\i} -- ++(.15, 0, 0) };

\foreach \a[evaluate={\v=70; \T=\v*sin(\a)/9.807*2;}] in {10, 20, ..., 80} {
\draw[x=(330:0.5pt), z=(90:0.5pt), Black, dashed]
plot [smooth, domain=0:\T, samples=50, variable=\t,
mark=*, mark repeat=2, mark size=1.8pt, mark options={fill=white, solid}]
(\v*\t*cos \a, 0, -9.807/2*\t^2+\v*\t*sin \a +0.1016) coordinate (end);
}
\end{tikzpicture}
\end{document}


• Great! And very beautiful....Why I not able to make the same thing :-((( ? I have understood your code....and I wait some days....for the bounty :-)....Great...all the best and thank you very much for my advice. Nov 10 '20 at 15:20
• In this question there is also the grass....tex.stackexchange.com/questions/495200/… I can put it and where? Nov 10 '20 at 16:02
• @Sebastiano For a 2d plot, grass effect is added on a straight line. For a 3d plot, it seems the grass effect should be added to a slanted rectangle, which I currently have no idea. Can you provide some sketch? Nov 10 '20 at 19:50
• @Sebastiano Such grass effect (various random plots in random color) in the form of vector graphics is, some sort of show off. I will try. Nov 10 '20 at 20:44
• @Sebastiano To be honest, I still have no idea about how to draw a simple but vivid grass effect in a slanted rectangle. Try filling the area with some grass image as a workaround? Nov 16 '20 at 23:42

The code you post answers almost all questions, at least the way I interpret them. All I did was to store v and alpha in "functions" and to use some double line trickery to get a different representation of the trajectory.

\documentclass[tikz,border=5]{standalone}
\usepackage[prefix=]{xcolor-material}
\begin{document}
\begin{tikzpicture}[x=(330:1cm),y=(30:1cm),z=(90:1cm),
declare function={v=70;% <- velocity (input)
alpha=30;% <- angle (input)
T=2*v*sin(alpha)/9.807;}]
\fill [LightGreen] (-1,-1,0) -- (-.5,1,0) -- (11,2,0) -- (11,-2,0) -- cycle;
\draw [Brown, thick, line cap=round] (10,0,0) -- (10,0,1);
\fill [Red] (10,0,1) -- (9.8,0,0.9) -- (10,0,0.8) -- cycle;
\fill [Yellow, shift={(7,0,0)}]
plot [domain=0:340, samples=20, smooth cycle, variable=\t]
(\t:rnd/16+0.25 and rnd/8+0.75);
\draw [x=(330:0.5pt), z=(90:0.5pt), Black, dash pattern=on 0.1pt off 4pt,
double,double distance=2pt,line cap=round]
plot [smooth, domain=0:T, samples=50, variable=\t]
({v*\t*cos(alpha)}, 0,{ -9.807/2*\t*\t+v*\t*sin(alpha)+0.1016})
coordinate (end);