Lost on Projectile motion problem

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To solve the projectile motion problem, the marble is thrown horizontally at 12.0 m/s from a building, and upon impact, it makes a 30.3° angle with the ground. The absence of air resistance means the horizontal velocity remains constant at 12 m/s. The vertical motion can be analyzed using kinematic equations to determine the height from which the marble was thrown. The key to solving the problem lies in calculating the time of flight and the vertical distance fallen. Ultimately, the height can be found by using the relationship between the horizontal distance traveled and the time it takes to fall.
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Homework Statement



A marble is thrown horizontally with a speed of 12.0 m/s from the top of a building. When it strikes the ground, the marble has a velocity that makes an angle of 30.3 ° with the horizontal. From what height above the ground was the marble thrown?


-im lost at where to begin

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The Attempt at a Solution

 
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I think the key in this question is whether or not you are ignoring air resistance?

Jared
 
yes, while ignoring the air resistance
 
If there is no air resistance, there is nothing acting to decelerate the ball in the horizontal plane. The balls horizontal velocity is a constant 12m/s.
 
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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