What takes longer? With airdrag or without?

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SUMMARY

The discussion centers on the impact of air resistance on the time it takes for an object shot vertically to return to the ground. Participants agree that while air drag affects the ascent of the object, it does not significantly delay the descent, particularly at high speeds. The analysis includes considerations of turbulent flow and drag scaling with the square of the speed. The conclusion is that air resistance does not extend the total time in the air for a bullet, even when accounting for different drag models.

PREREQUISITES
  • Understanding of basic physics concepts, particularly kinematics.
  • Familiarity with differential equations and their applications in motion analysis.
  • Knowledge of air resistance and its effects on projectile motion.
  • Experience with graphing functions to visualize motion dynamics.
NEXT STEPS
  • Research the effects of turbulent flow on projectile motion.
  • Study differential equations related to motion under varying drag conditions.
  • Explore the mathematical modeling of air resistance in high-speed projectiles.
  • Learn about the differences between linear and quadratic drag forces in physics.
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Physics students, educators, and anyone interested in the dynamics of projectile motion and the effects of air resistance on objects in flight.

nos
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Heey all,

Do you think it will take longer for an object shot from the ground vertically to reach to ground again with air resistance or without? Keep in mind, no air drag means it will go higher, but it won't be slower down on the way back.
 
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Assuming turbulent flow, drag scales with the speed squared - it is much more important on the way up than on the way down. I don't see any scenario where it would delay the bullet. Even with linear drag (proportional to the speed) I would be surprised if drag can make the bullet reach the ground later.
 
airdrag2.jpg
I tried to solve the differential equations and solve for the total time in the air. In this graph drag constant and gravity is set to 1. The variable x denotes the lift off velocity. So yeah, I think you are right, especially at high speeds.
 

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