Cork: Solving for the Height of a Cork in a Dropped Bucket of Water

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To determine the height the cork reaches in the water when the bucket hits the ground, the upward buoyant force and the cork's upward acceleration relative to the water must be analyzed. The downward acceleration of the bucket and the time it takes to fall from height h are also critical for calculating the cork's position. The cork's vertical position as a function of time needs to be established, considering the effects of buoyancy. The density of water is given as 1,000 kg/m³, which is relevant for calculating buoyant forces. The solution requires setting up equations based on these principles without needing numerical results.
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Please help! I need this within like 15 minutes!

Homework Statement


A cork is held at the bottom of a bucket of water of depth d.

The bucket is dropped from a height h, and simultaneously the cork is released. At the moment the bucket hits the ground, what height ill the cork have reached in the water?

Density of water = 1*10^3 kg m^-3

Homework Equations


Don't know...

I am in need of the equation, no numeical result.


The Attempt at a Solution

 
Last edited:
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GeneralShamu said:
Please help! I need this within like 15 minutes!

Homework Statement


A cork is held at the bottom of a bucket of water of depth d.

The bucket is dropped from a height h, and simultaneously the cork is released. At the moment the bucket hits the ground, what height ill the cork have reached in the water?

Density of water = 1*10^3 kg m^-3

Homework Equations


Don't know...

I am in need of the equation, no numeical result.


The Attempt at a Solution


1. What is the upward buoyant force (relative to the water)? What is the upward acceleration of the cork (relative to the water - ignore water resistance)? What is the vertical position of the cork (relative to the water) as a function of time?

2. What is the downward acceleration of the bucket and water? How long does the bucket take to fall to the ground?

3. What is the position of the cork at that time?

AM
 

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