Hello. I've got a simply ballistics program with a very simply algorithm to deal with air friction. However, I am trying to find a mathematical forumula equivalent. Here is the algorithm:(adsbygoogle = window.adsbygoogle || []).push({});

G = accel due to gravity (universal constant)

F = projectile air friction factor (constant for a given projectile)

T = delta T (delay between loops, varies depending on frame rate but is about 0.01)

Projectile starts out traveling at velocity Vo fired at angle Ao.

Velocity is broken into a vector made up of: Vx and Vy

Loop

Ax = Vx * F

Ay = Vy * F * G

V = [Vx*Ax*T, Vy*Ay*T]

Wait T

goto Loop

For any given projectile, I will know Vo and F.

For now, I want an equation where I can specify a point (x,0), and it will give me the required Ao so that the trajectory intersects that point.

Basically, given a specific distance, I want to know the angle required in order to land the projectile there (assuming the ground is flat and projectile is fired from y=0).

I the approach I'm trying to take is to find equations that give the projectile's current position (x,y) based on the variables Vo, Ao, and F, and the constant G. I can do this easily in an Excel spreadsheet, but I'm not sure how to do it in an equation.

I've come up with an acceleration forumula: Ax = Vx^2*F

Basic physics says that velocity is the integral of acceleration. However, I'm confused about if/how I can integrate this, since acceleration depends on velocity.

Can anyone help me out here? Thanks!

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# Converting an algorithm into an equation

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