Air resistance factor in projectile trajectory

This is a simple projectile (air resistance included) project I'm working on. The following initial conditions are given, x(0) = 0, x'(0) = v0*cos(theta), y(0) = 0, y'(0) = v0*sin(theta), v0 is the initial velocity given by the user.

I rewrote them to first order using the two initial conditions and made two functions:

function x = func_x(t, m, ar, v0, th)
x = (m/ar)*v0*cos(th)*(1-exp(-(ar*t)/m));

And,

 function y = func_y(t, m, ar, v0, th, g)
y = ((m/ar)*g+v0*sin(th))*(1-exp(-(ar*t)/m))-((m/ar)*g*t);

I did some experiments using a fixed mass (m, say 1), initial velocity (v0, say 100) and angle (th, say pi/4), and changing the air resistance factor gave a somewhat strange result. It appeared that the less air resistance I assign, the faster it drops. The graph look reasonable when I assign ar to be 1, and odd if I assign smaller value like 0.1. Is it supposed to happen, or did I do some mistakes somewhere?

The following code is used when I plot if it's needed.

t = linspace(0, 5, 200);
x = func_x(t, m, ar, v0, th);
y = func_y(t, m, ar, v0, th, g);
plot(x, y)

[Star Strider]

It seems logical to me that decreased air resistance would increase its maximum trajectory altitude, lengthen its distance of travel (range) and increase the speed it drops.

[John BG]

It's Physics basics of free fall in liquid gas: no matter the density of the fluid, if fluid density>0, if the fluid-object interaction generates drag, there is a maximum speed reached when drag equals opposing weight.

The speed does not increase all the time, if there is enough time before hitting bottom (of sea for a sinking vessel, of ground for falling object across atmosphere) the speed has a roof.

Obviously, the thinner the fluid, the higher is that maximum free fall velocity.

The heavier the falling object the faster the top speed will be reached.

To GG: why don't you share here the simulations you have done with different weights?

John

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[John D'Errico]

It is always good to see someone thinking about a problem, questioning the results. I don't that often choose to up-vote a question, but I did so here.

[CS Researcher]

It makes perfect sense. Air RESISTANCE is a force in the opposite direction which RESISTS the free motion. In your simulations, you can make everything constant except ar (assuming this is the variable for Air Resistance) and plot x as a function of ar. It will help you understand what kind of effect does Air Resistance have on the motion.