The path of a projectile fired from a gun is parabolic in a uniform gravity field with no air resistance. With air resistance, it's more closely elliptical (iirc not quite but this shouldn't bother you).

Suppose the muzzle velocity of the gun is V, at an angle "h" to the horizontal.

The horizontal speed (Vx) of the projectile will be V*cos(h) and the vertical (upward) speed (Vy) will be V*sin(h).

In every small time interval t, the vertical speed will change in a downward direction by an amount a*t where a is the acceleration due to gravity (9.81 meters per second squared near the surface of the Earth). Neglecting air resistance, the horizontal speed will remain constant. At the end of each time interval, the X coordinate will increase by Vx*t and the Y coodinate will increase by Vy*t. Note that as the projectile finishes rising and starts to fall, Vy will become negative (denoting a change in direction).

This may be the form in which the program is best written, but the actual coordinates of the projectile at time t will be

X = X0 + (V * cos h) * t

Y = Y0 + (V * sin h) * t - a*t*t/2

[alternatively, Y = Y0 + t * (V * sin h - a * t/2)]

Where V is the initial muzzle velocity, (X0,Y0) is the initial position of the projectile (i.e. the gun's position), t is the current time, and a is the acceleration due to gravity (9.81 metres per second squared near the surface of the earth). Some formulations say that a is (-9.81) and change the sign before the a in the formula to "+" instead of "-".

If you want to take into account the effect of air resistance, there is a decelerating component proportional to v-squared and a component proportional to v. The former is much larger. There's no point modelling the component proportional to just v if all you want is visual realism.

To take into account wind drag, add to the horizontal distance moved a small extra distance term proportional to the wind speed at each time step. Not quite physically realistic, but good enough I expect.

Suppose the muzzle velocity of the gun is V, at an angle "h" to the horizontal.

The horizontal speed (Vx) of the projectile will be V*cos(h) and the vertical (upward) speed (Vy) will be V*sin(h).

In every small time interval t, the vertical speed will change in a downward direction by an amount a*t where a is the acceleration due to gravity (9.81 meters per second squared near the surface of the Earth). Neglecting air resistance, the horizontal speed will remain constant. At the end of each time interval, the X coordinate will increase by Vx*t and the Y coodinate will increase by Vy*t. Note that as the projectile finishes rising and starts to fall, Vy will become negative (denoting a change in direction).

This may be the form in which the program is best written, but the actual coordinates of the projectile at time t will be

X = X0 + (V * cos h) * t

Y = Y0 + (V * sin h) * t - a*t*t/2

[alternatively, Y = Y0 + t * (V * sin h - a * t/2)]

Where V is the initial muzzle velocity, (X0,Y0) is the initial position of the projectile (i.e. the gun's position), t is the current time, and a is the acceleration due to gravity (9.81 metres per second squared near the surface of the earth). Some formulations say that a is (-9.81) and change the sign before the a in the formula to "+" instead of "-".

If you want to take into account the effect of air resistance, there is a decelerating component proportional to v-squared and a component proportional to v. The former is much larger. There's no point modelling the component proportional to just v if all you want is visual realism.

To take into account wind drag, add to the horizontal distance moved a small extra distance term proportional to the wind speed at each time step. Not quite physically realistic, but good enough I expect.