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One problem with your statement is that air resistance (drag) is a function of velocity. The faster an object travels, the more air resistance it encounters. Therefore, strictly speaking, it cannot be said that gravity and air resistance are independent--acceleration due to gravity changes object velocity, which in turn changes air resistance.
Omar is essentially correct, in the Newtonian model. Oosty's statement is only true in vacuum, and the omission of this critical condition makes the statement incorrect. It is also inapplicable to high-velocity scenarios because, as we all know, objects dropped from the sky don't fall through vacuum, but through air.
A more precise (and correct) formulation of Oosty's statement might read: "For objects on Earth, the acceleration due to gravity experienced by an object is independent of its mass. A brick and a penny dropped simultaneously from the same height in vacuum will hit the ground simultaneously."
Furthermore, Omar refers to momentum--though he does not call it as such--as another important consideration. At a given fixed velocity, a massive object carries proportionally more momentum than a less massive object. This, combined with the law of conservation of momentum, explains why an impact with a brick is far more energetic than an impact with a feather at the same velocity.
Hah, I knew that when I wrote it, but figured nobody would call me on it. Think of it this way, air resistance is dependent on speed caused by acceleration due to gravity, but gravity is not dependent on air resistance. Gravity is a consequence of two mass attracting each other, in this case the camera, and the earth. Drag is a consequence of an object moving through a fluid or gas. So it doesn't matter if an object is falling in a vacuum or maple syrup, the pull of gravity is the same, but the opposing force, drag, increases. A vacuum is just the easiest model to work with. In entry-level physics classes all problems will assume you're working with ideal gases/fluids, frictionless pulleys, frictionless surfaces, mass-less strings etc. Of course none of these things exist in real life, and must be taken into consideration when doing realistic calculations, but the underlying principles remain the same.
Lol, sorry for all that. The way you rewrote Oosty's statement is correct, I just wanted to clear up the first part.
You're right about the last part, and comes from Newton's second law of motion, simply F = mass * acceleration. And kinetic energy = .5 * mass * velocity^2
So like you said, an objects energy increases with mass and velocity.
Sorry, I'm a bored college student.