Drag and weight

Weight is proportional to mass, and so the full water bottle has a greater weight force than the empty bottle. The acceleration due to weight does not change with mass though, as acceleration is inversely proportional to mass (and mass component in the acceleration equations is cancelled out).
The drag force is only affect by the surface of the object, and is not affected by the mass of the object. However, because it is constant, two object with the same drag and different masses will experience different accelerations, with the heavier object experiencing less acceleration.
Because of this, the full water bottle experiences the same downwards acceleration as the empty bottle, but less upwards acceleration, making it fall faster.

Their drag coefficients are the same since they are externally identical, and so the upwards drag force will be the same for any given velocity
F=m*a => a=f/m
Therefore the bottle with greater mass will decelerate less due to drag for an overall greater downwards acceleration
Consequently the full bottle hits the ground first

But is the difference still fairly negligible?

Only if the factors involved are negligible but that's not what the question was now was it
Drop it from a tower and the difference should be obvious

So I'm wrong.... I can't let him know this though.

Thanks Veeky Forums!

I don't think weight is part of what determines the drag force. Here's a snapshot of the relevant section from wikipedia. When they say the density of the "fluid" in this case that means the air. The other factors in the equation besides the air density are speed of the object and stuff about the object's size and shape.

If that drag force wasn't there (or is so small that you can ignore it for all practical purposes) then two objects will hit the ground at the same time.

With the full water bottle the drag force is tiny but with the empty one it might be affecting it a little, causing it to hit the ground slightly later than the full one.

If you want to demonstrate two objects hitting the ground at the same time, try a pebble vs. a huge boulder. Neither of those will be affected by air drag too much.

Also weight =/= mass. Mass is measured in kg and an intrinsic property of the object. Weight is the force of gravity acting on a mass. weight=mass*g where g is gravity on the Earth. Our weight on a scale is a measure of how strongly Earth is pulling our intrinsic mass down. Your weight on another planet would be different, but your mass would be the same.

dropping from arm height would be hard to tell the difference. but a slightly higher height of drop, i'm guessing the magnus effect would start pulling and pushing the non-filled water bottle around and take away it's downward velocity. the filled bottle would be more resistant to extreme direction changes from magnus effect and hit the ground sooner. i'd bet if you set up a high speed camera and make sure you drop both bottles from the same height at the same time, you'll see the filled bottle hit ground first.

If they tumble due to.wind or some other factor, could the change in trajectory cause one to hit before another? I assume the lighter one would be more affected by this. If you took that variable out would the difference be relatively small?

Just a /b/tard here don't take my advice

The object is moving towards the Earth and the Earth is moving towards the object. That's how gravity works.

this is a good explanation.