Finding displacement from PE and KE?

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The discussion revolves around calculating the total distance a diver falls from a diving board to their stopping point underwater, given their mass and the net force exerted by the water. The key concepts involve using kinetic energy (KE) and potential energy (PE) equations to find the diver's initial velocity and displacement. The diver's potential energy at the top is converted to kinetic energy as they fall, and the upward force from the water decelerates them. By applying the equations of motion and force, the total distance from the diving board to the stopping point underwater is determined to be 20.3 meters. Understanding the relationship between KE, PE, and the forces involved is crucial for solving similar problems.
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Homework Statement


We were assigned bookwork, we have a test on thursday, and I really don't understand the concepts of the lesson or what we are suppose to be doing. (My teacher is not the best by any standards.) Anyhow, here is the problem.

" A 50.0 kg diver steps off a diving board and drops straight down into the water. The water provides an upward average net force of 1500 N. If the diver comes to rest 5.0 m below the water's surface, what is the total distance between the diving board and the diver's stopping point under water? "

Homework Equations


KE = 1/2mv^2
PE = mgx

The Attempt at a Solution


I'm confused on the entire concept of Kinetic and Potential energy. In this problem it says I need to find the divers point underwater? The only thing I can think of is solving for Ek and then Ek equals PEg, and solve for displacement, but I don't have velocity, I asked my teacher for help, and he says those are the only equations we needed, even though later he said he hadn't even looked at the problem he'd assigned.. Any help is much appreciated, not only on this specific problem but concept wise as well.
 
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at the top of the board, the diver has PE = mgh
at the bottom, he has KE = (1/2)*m*v^2 = mgh
it takes a 1500 N force 5 meters to decelerate a 50 kg mass traveling at v
so, you can find the initial velocity
so you can find the KE
set that equal to the PE, and solve for h
add 5
 
Oh yeah! I can do F=ma to get acceleration and plug that into V = ax +vi to get my velocity, and it says when the diver stops, so that's why you add 5 to the end to get 20.3 m . Thanks!
 
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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