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11) When we solved problems dealing with objects in free-fall, we often exploited a symmetry that...

11) When we solved problems dealing with objects in free-fall, we often exploited a symmetry that led to the conclusion that the time it takes an object to go from a starting height to a maximum height (where the vertical (y-direction) velocity is zero) is the same as the time that it takes for the object to fall from that maximum height back to the starting height. If we introduce air resistance as a force similar to a friction force, does that change the symmetry between the time to the top of the trajectory and the time to fall down to the starting height? (note that air resistance is a little more complicated than a constant force like friction, but that simplification won’t change our answer here if we speak in general terms)

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