Projectile motion with air resistance

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SUMMARY

The discussion focuses on simulating projectile motion with air resistance, specifically where the resistance is proportional to the square of the velocity. The user is developing a program that requires input for horizontal and vertical velocity components but encounters challenges due to the reliance on mass in existing equations. A key insight shared is to simplify the problem by using the ratio of air resistance constant k to mass m, denoted as c=k/m, allowing the mass to be disregarded in calculations. Additionally, it is noted that in one-dimensional motion, the velocity as a function of time, v(t), can be solved directly.

PREREQUISITES
  • Understanding of basic physics concepts related to projectile motion
  • Familiarity with air resistance modeling, specifically the equation Fd=-kv²
  • Knowledge of Newton's second law, ƩF=ma
  • Proficiency in programming for simulation and graph plotting
NEXT STEPS
  • Research the derivation and application of the equation Fd=-kv² in projectile motion simulations
  • Learn how to implement numerical methods for solving differential equations in programming
  • Explore techniques for graphing motion trajectories in programming environments
  • Investigate the implications of varying the air resistance constant k in simulations
USEFUL FOR

This discussion is beneficial for physics enthusiasts, software developers working on simulation projects, and educators looking to enhance their understanding of projectile motion dynamics with air resistance.

denham
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Hey guys, I am in the process of writing a program for pmotion with air resistance that is proportional to the velocity squared and I've hit a stump. In my program it simulates the path of the ball by changing the time and putting it into the equation and plotting it on a graph. My problem is all the equations i have found using air resistance has mass. I know this question is not 100% physics but if anyone could help It would be greatly appreciated

The program allows only the input of the horizontal velocity component and the vertical velocity component

Thanks
 
Last edited:
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You have Fd=-kv², and you have ƩF=ma. All that really affects the motion here is the ratio k/m. Call it some constant c=k/m, and then you don't have to worry about the mass.

By the way, in 1D, you can solve for v(t) directly.
 

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