Let’s look at some of the different relevant funtions associated with projectile motion in the scenarios where air resistance starts to be a factor.  We’ll start with a scenario in which the resistive drag is linear (low Reynolds number scenario).  We find the following (x position as a function of time with linear drag bv).

Manipulate[Plot[ (m vx / b) (1-Exp[-b t/m]),{t,0,10}],{{m,1.5},1,10},{{b,.2},0.01,5},{{vx,40},0,100}]

Now let’s explore the y velocity as a function of time with linear drag bv)

g:= 9.81

Manipulate[Plot[Exp[-b t/m] (vy- (m g / b)) + (m g / b),{t,0,100}],{{m,1.5},1,10},{{b,.2},0.01,5},{{vy,-40},-100,100}]

And the y position as a function of time:

Manipulate[Plot[(m/b) ( (1-Exp[-b t/m]) (vy-(m g / b)) + g t),{t,0,10}],{{m,1.5},1,10},{{b,2},0.01,5}, {{vy,-40},-100,100}]

And finally, we have the actual trajectory (horizontal/vertical):

Manipulate[Plot[((vy + (m g / b))/vx) x + ((m g / b) m / b) Log[1 - b x / (vx m)],{x,0,100}],{{m,1.5},1,10},{{b,2},.01,5},{{vx,40},0,100},{{vy,40},-100,100}]

Vertical Quadratic Drag.....

Manipulate[Plot[Sqrt[m g / c] Tanh [ArcTanh[v0 Sqrt[c / (m g)]] - t Sqrt[(c g)/m]],{t,0,5}],{{m,1.5},1,10},{{c,.15},.01,.3},{{v0,7},-10,10}]