Simulating Thrown Sphere: Find X,Y Positions & Add Drag Force

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To simulate a sphere thrown in the air while accounting for drag, the equations for x and y positioning must be adjusted. Drag, which opposes the motion and depends on speed, should be incorporated into the calculations of forces acting on the sphere. Using Euler integration is recommended for a computer simulation, allowing for frame-by-frame calculations of forces, velocity, and position. By adding a force proportional to the velocity, drag can be effectively modeled. This approach enhances the accuracy of the simulation.
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I'm trying to simulate a sphere got thown in the air
I have find the way of knowing x,y positioning of the sphere though this equation:
x(t) = vt cos(theta)
y(t) = vt sin(theta) - (gt^2)/2
Where v is the initial velocity, theta is the angle, t is the time and g is the gravity.

But this does not take into account of the drag, what if there is drag?
suppose I know the force of drag, where should I add in the 2 functions above?
 
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Drag acts in the (opposite) direction of the object, and is a function of the speed.
 
Are you simulating this on a computer? If so then the easier and more flexible approach would be to use integration. You could start with Euler intergration (google it). You basically calculate the forces on the ball each frame, use that to get the velocity and use that to change the position of the ball. YOu can easily add drag by adding a force proportional to the velocity.
 
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