How to Factor Air Resistance into Basketball Trajectory Calculations?

[gex]

Hi all, I will be doing an experiment in which I will be rolling a basketball down an elevated ramp. After leaving the ramp, the basketball will free fall for 1.25m before reaching the ground. I was looking to come up with a theoretical trajectory for the motion of the ball, the issue is that I am not sure how I would go about factoring in air resistance into my calculations. Any starting points would be much appreciated.

-Thank you in advance

 

[houlahound]

Drag is proportional to speed, I don't believe it will be a factor in your set up.

 

[gex]

I calculated that the ball will have an impact velocity of 5.58 meters per second, so in your opinion the velocity is too low to be greatly affected by air resistance?

 

[houlahound]

Really depends on what level of accuracy is required and the uncertainties in the whole experiment.

How you going to measure the speed or time of flight?

 

[gex]

Tracking software will be used to measure speed and time of flight, but in an attempt to increase my grade I want to theoretically calculate the motion of the ball to backup my hypothesis, I know how to do this without air resistance being a factor but am struggling in finding a method to factor it into my calculations to make my theoretical model as accurate as possible. Thank you for your replies houlahound.

 

[houlahound]

Why don't you do some test runs and see how far the measured results are a way from the theory.

What are the errors/uncertainties in your measurement tracking vid.

 

[houlahound]

Keep in mind you have a spinning falling ball with a horizontal velicity component, very complex air flow.

 

[gex]

I'm not quite sure how I would go about calculating the uncertainty of the tracking, and my issue is that i do not know how I would include air resistance in my theory. Because the velocity of the ball is constantly changing during its fall, I have no clue how I would account for the force of air resistance in my calculations.

 

[houlahound]

There are models that account for air resistance, not simple math. I think you need to make an empirical model by seeing how far from ideal (no resistance) you are.

ETA, the standard models are;

Low speed, drag proportional to speed

High speed, drag proportional to speed squared.

 

[gex]

I see, I will probably just give up on the idea of air resistance as I'm only in high school haven't learned calculus yet. I will just stick to assuming no air resistance for my model. Thanks for your help houlahound.

 

[houlahound]

Well you haven't determined if you have a problem yet until you compare the basic theory with your measurement.

You will achieve more by justifying your no drag assumption.

Good luck.

 

[anorlunda]

Tracking software will be used to measure speed and time of flight, but in an attempt to increase my grade I want to theoretically calculate the motion of the ball to backup my hypothesis, I know how to do this without air resistance being a factor but am struggling in finding a method to factor it into my calculations to make my theoretical model as accurate as possible. Thank you for your replies houlahound.

Drag varies as the square of speed. So if you add drag to the force balance, it will be a constant times speed squared. you have accounted for drag. But if the constant is small, it does not change the results much.

Estimate the constant by a guess that the terminal velocity is 120 mph (176 fps). At terminal velocity, drag force equals weight.
But at your speed, drag will be only 0.0017 times the weight. That is negligible, but you will have accounted for it. If someone challenges your arbitrary guess of 120 mph, repeat the calculation with 240 mph and 60 mph as the assumed terminal velocity and show that the end result does not change significantly. Drag is insignificant with all three guesses of terminal velocity.Good luck

 

[gex]

Thank you so much for helping guys :)