# Deceleration of a projectile (With air resistance)

1. Jun 8, 2013

### 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 lets 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

2. Jun 8, 2013

### Staff: Mentor

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.

3. Jun 8, 2013

### 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. Infact we have done SUVAT and my curiosity lead me to studying this myself. It is more complex than I'd imagined.

4. Jun 8, 2013

### Staff: Mentor

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?

5. Jun 8, 2013