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xtraboi

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**Mentor note**: Moved from a technical forum section, so Homework Template is not present.

Hello Physics Forums members,

I am a student in AP Physics C and I was just working out the range of a projectile when air resistance is non-negligible. As of right now I'm going to use the linear model of air resistance to simplify calculations (F_air = -bv).

When drawing the Free Body Diagram for the projectile, I know that the force on the object due to air resistance opposes the direction of motion, so does that mean there would be one Free Body Diagram when the projectile is going up and another when the projectile is going down?

If that's the case, how would I go about finding the total range of the projectile?

My approach is to use the kinematic equation v_f^2 = v_i^2 + 2*a*d twice (one for when the object is going up, and one for when the project is coming down) and substitute the acceleration as calculated from the Free Body Diagram, but I'm not sure if that's the right approach as the force due to air resistance is dependent on the instantaneous velocity at a point. I'm thinking to maybe take the average value of the force due to air resistance, but I'm not even sure what integral would achieve that as we haven't covered what I'm doing in class.

Thanks in advance.