The acceleration of the bottle is [tex]g=9.8 m/s^2[/tex] downward
Explanation:
When an object is in free fall (=only the force of gravity is acting on it), its acceleration is equal to the acceleration of gravity.
In fact, the only force acting on the object is the force of gravity, whose magnitude is:
[tex]F=mg[/tex]
where
m is the mass of the object
[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity
According to Newton's second law, the net force on the object is equal to the product between its mass (m) and its acceleration (a), so
[tex]F=ma[/tex]
By combining the two equations, we get
[tex]mg=ma\\a = g[/tex]
Therefore, the acceleration of any object in free fall (and so, also of the bottle in the problem) is [tex]g=9.8 m/s^2[/tex].
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