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I feel like this does not necessarily fit the format of a homework problem perse, but I am not sure where else to ask, but—

I was doing a thought experiment of a trajectory with air resistance (Air-resistance being proportional to the velocity with some constant), and was thinking to solve it doing force body diagrams. I was curious, would you have to do two force body diagrams in the y-direction due to air resistance changing direction? One for when the projectile is moving upward, and one when it is falling back down? Therefor you must ultimately integrate two different functions to find the time it takes? Adding the time it takes to get to y_max, then from there to y=0 to find the total time?

Or perhaps I am just unfamiliar with how integrals work entirely, and that when I integrate I am already taking into account that air resistance is a function of time, regardless of it changing directions in finality. Actually I think I just answered my question. :P

I was doing a thought experiment of a trajectory with air resistance (Air-resistance being proportional to the velocity with some constant), and was thinking to solve it doing force body diagrams. I was curious, would you have to do two force body diagrams in the y-direction due to air resistance changing direction? One for when the projectile is moving upward, and one when it is falling back down? Therefor you must ultimately integrate two different functions to find the time it takes? Adding the time it takes to get to y_max, then from there to y=0 to find the total time?

Or perhaps I am just unfamiliar with how integrals work entirely, and that when I integrate I am already taking into account that air resistance is a function of time, regardless of it changing directions in finality. Actually I think I just answered my question. :P

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