# Deceleration of a projectile (With air resistance)

• SirAmikVarze
In summary, the conversation discusses the problem of modeling the flight of a bullet, taking into account air resistance. The equation for drag force is provided and the question is raised on how to use this value to model the flight path over time. The conversation also touches on the relationship between drag force and acceleration, and the use of differential equations in solving the problem. Approximations and the role of mass in the formula for drag are also mentioned. Recommendations are given to use the height from the ground at the point the bullet leaves the barrel and the wikipedia article on ballistics for further assistance.
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

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.

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.

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?

## 1. What is deceleration of a projectile?

Deceleration of a projectile is the decrease in velocity of a projectile as it travels through the air. This is caused by air resistance, which is the force that opposes the motion of an object through the air.

## 2. How does air resistance affect the deceleration of a projectile?

Air resistance increases as the speed of the projectile increases. This means that as a projectile moves faster, it will experience a greater deceleration due to air resistance. As the projectile slows down, the air resistance decreases and the deceleration also decreases.

## 3. Is deceleration of a projectile affected by the weight or mass of the object?

Yes, the weight and mass of a projectile can affect its deceleration. Heavier or more massive objects will experience a greater deceleration due to air resistance compared to lighter objects. This is because air resistance is directly proportional to the surface area and velocity of the object, but inversely proportional to its mass.

## 4. Can the shape of a projectile impact its deceleration?

Yes, the shape of a projectile can affect its deceleration. A more streamlined shape will experience less air resistance and therefore have a slower deceleration compared to a less streamlined shape. This is because a streamlined shape can better deflect air molecules and reduce the force of air resistance.

## 5. How can we calculate the deceleration of a projectile with air resistance?

The deceleration of a projectile with air resistance can be calculated using the equation: a = (F - Fair) / m, where a is the deceleration, F is the force applied to the projectile, Fair is the force of air resistance, and m is the mass of the projectile. It is important to note that this equation is an approximation and may not account for all factors that affect deceleration in real-world situations.

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