Deceleration of a projectile (With air resistance)

[SirAmikVarze]

Hi there, sorry for asking a question as my first post instead of contributing to the community however I have a problem which I just cannot seem to find an answer to.

I am trying to model the flight of a bullet when taking into account air resistance and I am using this equation to get the drag force of the bullet at certain velocities:

D = \frac{ρ*V^2*Cd*A}{2m}

Where:
D is the drag force in Newtons
ρ is the density of air (1.225 kg/m³)
V is the velocity of the bullet
Cd is the drag coefficient of the bullet (For this let's just assume it's 0.12)
A is the cross sectional area of the bullet (Also for this let's say it's 0.05m²)
m is the mass of the bullet (And let's assume this is 0.150kg)

How would I use the value of the drag force of the bullet to model the flight path over time?
In my head I'm sure it's something simple which I have studied before but I just can't think what it might be

Thank you in advance :)

 

[mfb]

If you can neglect gravity:
How are the drag force and acceleration of the bullet related?
You can modify your equation to a differential equation, and solve that.

 

[SirAmikVarze]

Since this is rough calculation I will be using the height from the ground at the point the bullet leaves the barrel as 1.5m, this gives me a flight time of 0.553 seconds when I don't take into account factors which would provide lift.

The drag force and acceleration are related as such that the drag force on the bullet (with an initial velocity of 600ms^-1 at the end of the barrel) causes the bullet to decelerate over the 0.553 seconds in flight, what I need to find out is the distance traveled by the bullet in the 0.553 seconds it is in flight.

Please excuse my lack of knowledge with mathematics here, I am only 16 so haven't studied differential equations yet. In fact we have done SUVAT and my curiosity lead me to studying this myself. It is more complex than I'd imagined.

 

[mfb]

Okay, then approximations will be better.
What is the initial deceleration of the bullet?
Assuming this stays constant over the whole flight duration (=first approximation), what is the final velocity of the bullet?
What is the deceleration at that final velocity?
Can you improve the first approximation, based on that?

 

[Aero_UoP]

Why do you have the mass in the formula for the drag?

The wikipedia article on ballistics should be helpful in your case:
https://en.wikipedia.org/wiki/External_ballistics