Can’t flip direction of ball without messing up gravity

you are not really doing reflection … to reflect by major axis you should negate the appropriate coordinate of the speed vector (and correct the position) I do not see such behavior in your code. Instead your y velocity has no sign regardless of the direction up/down hence you just add gravity acc to it … to remedy either rewrite the code or add the yreflection to your gravity related code too… also you got theta? I would expect angle only in the first shooting

see

• Bouncing Ball Making it slow down at peak of height

• My Algorithm to Calculate Position of Smartphone – GPS and Sensors

• pendulum simulation

  You just use/add forces you want to use. But in your collision once you detect you are inside wall you need to correct the position along with the reflection of speed too otherwise you risk double collisions …

Here small C++ example with air friction:

//---------------------------------------------------------------------------
double pos[2],vel[2],acc[2],r;  // ball
double x0,y0,x1,y1;             // walls
//---------------------------------------------------------------------------
void ball_update(double dt)
    {
    int i;
    double v,k=0.0001,g=9.81;
    dt*=10.0;                                   // time multiplier for simulation speed ...
    // compute driving force/acceleration
    v=sqrt((vel[0]*vel[0])+(vel[1]*vel[1]));    // |vel|
    acc[0]=  -(k*vel[0]*v);                     // gravity + air friction (k*vel^2)
    acc[1]=+g-(k*vel[1]*v);
    // Newton/D'Alembert simulation
    for (i=0;i<2;i++) vel[i]+=acc[i]*dt;
    for (i=0;i<2;i++) pos[i]+=vel[i]*dt;
    // colision/reflect
    if (pos[0]<x0+r){ pos[0]=x0+r; vel[0]=-vel[0]; }
    if (pos[0]>x1-r){ pos[0]=x1-r; vel[0]=-vel[0]; }
    if (pos[1]<y0+r){ pos[1]=y0+r; vel[1]=-vel[1]; }
    if (pos[1]>y1-r){ pos[1]=y1-r; vel[1]=-vel[1]; }
    }
//---------------------------------------------------------------------------
void ball_init()
    {
    Randomize();
    pos[0]=0.5*(x0+x1);
    pos[1]=0.5*(y0+y1);
    double a=2.0*M_PI*Random(),v=50.0;
    vel[0]=v*cos(a);
    vel[1]=v*sin(a);
    r=20.0;
    }
//---------------------------------------------------------------------------

My coordinate system is (0,0) is top left and x point right and y points down …
To use this just init the walls x0,y0,x1,y1 call the ball_init() and then in some timer call ball_update(dt) and render ball at pos and radius r …

This is how it look like:

PS. You need to tweak the parameters like delta time dt, accelerations or add pixel scale to match your needs… You need to have all units compatible … I recommend using SI (m,m/s,m/s^2,s,N,.. ) so you also need to decide how big is pixel (in meters)