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Tracker Modelling Skydiving with Parachute Opening by Evergreen Sec Tan Kim Kia

 
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Reference:

http://tankimkia.blogspot.sg/2015/10/modelling-skydiving-with-tracker.html?spref=fb

 https://drive.google.com/folderview?id=0Bw72rpuy2MMLRUFtM1c1VzM2Rk0&usp=sharing#

Modelling Skydiving with Tracker Software

 
Following my last post explaining the skydiving, here it comes the Skydiving Modellingusing TRACKER Software.  


Notes for teachers and learners who would like to use this TRZ file.
The fy is parameterize for the ease of modelling.
m = mass of human body
A_h = surface area of human body
A_p = surface area of parachute
g at 2000 m height
d = density of air
Cd = drag coefficient of human body
Cd2 = drag coefficient of parachute
g2 = g near surface of Earth
T – duration for parachute opening in Model A

Model A(Red):  Parachute opens slowly over T seconds

 

Fy = if(t<35,m*g-A_h*0.5*d*Cd*vy^2,if(t<55,m*g-0.5*d*Cd2*A_p*vy^2,if(vy>0,-m*g,0)))

  

Model B(Blue): Parachute opens fully immediately T = 0

  

Fy = if(t<35,m*g-A_h*0.5*d*Cd*vy^2,if(t<35+T,m*g-0.5*d*Cd2*(A_h+(t-35)/T*A_p)*vy^2,if(t<55,m*g-0.5*d*Cd2*(A_h+A_p)*vy^2,if(vy>0,-m*g,0))))

 
Velocity-time graph for Model A:


Velocity-time graph for Model B:


Comparison of Velocity-time graph for Model A & B:








Acceleration-time graph - Model B compared to Model A    

 Conclusion

Model A’s deceleration is 3.1g, which is realistically small, and therefore, it is believeable the correct answer? 
Model B has a deceleration of 17g, which is unrealistic big and likely to cause hurt on the parachutist, which is the examiners answer of B.
I think it is a bad idea to open the parachute immediate while the parachutist is falling at 40 m/s. In real life, according to a Discovery Education Channel video (https://www.youtube.com/watch?v=ur40O6nQHsw), the parachute takes about 2-3 seconds to open fully, linking back to Singapore O Level Physics question: 5058/2010/P1 Q3, the answer is still C. What do you think? post your comments and discuss!

Ideas for teaching and demonstration:

Adjust the parameters and compare the velocity-time graph and acceleration-time graph. 
Download the Tracker zip file for Skydiving Modelling. 
You may find the free TRACKER Software at http://www.cabrillo.edu/~dbrown/tracker/
Related Singapore O Level Physics question: 5058/2010/P1 Q3
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Parent Category: 03 Motion & Forces
Category: 02 Dynamics
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