Biomechanics - CoG and projectile motion

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In a basketball jump scenario, both players have identical mass and body dimensions, taking off with the same velocity. However, Player A, who raises both arms, has a different center of gravity (CoG) compared to Player B, who raises only one arm. The CoG shifts upward when an arm is raised, allowing Player A to achieve a higher effective jump height. This principle mirrors advancements in high jumping techniques, where optimizing body positioning significantly enhances performance. Ultimately, the distribution of mass and the position of the CoG play crucial roles in determining the advantage in jumping ability.
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Two basketball players jump for the ball. Both players have exactly the same mass and exactly the same body segment dimensions. Both players also take-off with exactly the same vertical and horizontal velocity of their center of gravity (CoG). Player A jumps up and reaches for the ball with both arms, while player B reaches for the ball with one arm (the other arm is down by her side). I need to use my knowledge of projectile motion and the factors that affect the location of the CoG to explain why the player that has one up arm up has an advantage and explain it in at least 1 page of writing.



initial kinetic energy = 1/2mv^2 where v equals the initial velocity of the player jumping up and m equals mass



This is what I have so far: The forces for both basketball players are the same. The height of CoG will be the same for both players. Potential energy is equal to the initial kinetic energy. The position of the CoG depends on the distribution of mass. When both arms are down, CoG is somewhere in the middle section of both basketball players.
 
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So what happens to the center of mass when one arm is raised and when both arms are raised? A very similar principle in used in high jumping and actually made a huge increase in the height jumpers could achieve when a new technique was mastered.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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