Deceleration of a projectile (With air resistance)

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Discussion Overview

The discussion revolves around modeling the flight of a bullet while considering air resistance. Participants explore the relationship between drag force, acceleration, and the bullet's flight path over time, incorporating mathematical modeling and approximations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant presents an equation for calculating drag force, expressing uncertainty about how to use it to model the bullet's flight path over time.
  • Another participant suggests that the drag force and acceleration are related and proposes modifying the drag equation into a differential equation for further analysis.
  • A participant shares a rough calculation for flight time and expresses the need to determine the distance traveled by the bullet during its flight, indicating a lack of familiarity with differential equations.
  • Another participant questions the inclusion of mass in the drag force formula and references a Wikipedia article on ballistics for additional context.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best approach to model the bullet's flight, and multiple viewpoints on approximations and the role of mass in the drag formula are presented.

Contextual Notes

Participants express varying levels of mathematical knowledge, with some lacking familiarity with differential equations, which may limit their ability to fully engage with the proposed modeling techniques.

Who May Find This Useful

This discussion may be useful for individuals interested in ballistics, physics modeling, or those seeking to understand the effects of air resistance on projectile motion.

SirAmikVarze
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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 :)
 
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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?
 

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