A plastic ball is held at the bottom of a bucket of water and then released. As it is released, the bucket is dropped over the edge of a cliff. What happens?

Initially, the plastic ball is submerged in water and held at the bottom of the bucket. Two primary forces are acting on the ball: the buoyant force (upward direction) and the gravitational force (downward direction). The buoyant force is given by: F_b = ρ_water * V_ball * g where ρ_water is the density of water, V_ball is the volume of the ball, and g is the acceleration due to gravity. On the other hand, the gravitational force acting on the ball, also known as weight, is given by: F_g = m_ball * g where m_ball is the mass of the plastic ball. Since the ball is held in place, the net force acting on it is zero. But once it is released, the ball will experience a net buoyant force that will push it upward since F_b > F_g (as it is a plastic ball).

When the bucket is dropped off the cliff, both the bucket and the ball fall freely under the influence of gravity. They experience the same acceleration due to gravity (g). Since there is no additional force acting on the water inside the falling bucket in the vertical direction, there won't be any upward buoyant force on the ball.

As there is no buoyant force acting on the ball while the bucket is falling, the ball will also be in free fall along with the water and the bucket. The gravitational force acting on the ball will be the same as the gravitational force acting on the water and the bucket. Therefore, the ball, water, and the bucket will fall at the same rate, and thus the plastic ball will remain submerged and appear to float inside the bucket as they all fall together. So, when the bucket containing the ball and the water is dropped, the ball will remain submerged in the water and they will "float" inside the bucket while falling towards the ground.