Hi there
How do i make calculations of projectile motion with the consideration of air resistance/ drag forces? And would the calculations including air resistance differ immensely compared to theoretical caclucations with no air resistance?
Hello! So if you do want to do that (don't need to in this course!) there are a few ways you can do it, depending on how accurate you want to be with things
Air resistance is generally modelled as being proportional to the square of velocity. The constant of proportionality is the
drag coefficient, and is different depending on the object, its inclination, all sorts of stuff. I've seen \(C=0.5\) used a fair bit, I think it might be the standard one for spherical objects?
So the idea is you calculate the air resistance by taking the velocity \(V\) (the vector sum of horizontal and vertical velocities), calculating the resistive acceleration as \(a_\text{res}=0.5V^2\), and then redistributing that to the two directions.
Where \(\theta\) is the velocity angle at that point in time! As you can see, it gets complicated quickly! The other thing you can do is just add a constant horizontal deceleration to the object, which effectively turns your horizontal calculations into ones with acceleration just like the vertical. And there are more - It depends on how close you want to be to reality
Edit: How much will it differ? Again, depends. Try and calculate the motion of an airplane without air resistance and things break pretty quickly! For most everyday situations with aerodynamic objects, you are fine. For example, I did an experiment with my Tutesmart class to predict the landing position of a hot wheels car launched from a ramp. The theoretically predicted position was exactly where the car landed