What takes longer? With airdrag or without?

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An object shot vertically will reach the ground faster without air resistance than with it, as air drag significantly affects the ascent more than the descent. The discussion highlights that drag scales with the square of the speed, making it a critical factor during the upward motion. Even with linear drag, it is unlikely that air resistance would delay the object's return to the ground. The analysis of differential equations supports the conclusion that at high speeds, drag does not prolong the time in the air. Overall, the consensus is that air resistance does not increase the time for the object to hit the ground.
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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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