Word Problem with Kinematics Equation

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The discussion revolves around solving a kinematics problem involving an object thrown from a cliff. The object starts with an initial velocity of 10 m/s upwards and lands with a velocity of 20 m/s downwards, with gravity acting at 9.8 m/s². The participant is unsure how to calculate the displacement, which the answer key states is -15 m. They have attempted to find the time of flight, calculating it to be approximately 3.1 seconds. Guidance is provided to use the kinematic equations without rounding the time to accurately determine the displacement.
Natko
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Homework Statement


An object thrown up from a cliff 10 m/s reaches a velocity of 20 m/s [down] as it lands. If acceleration due to gravity is 9.8 m/s2, what is the object's displacement? How long did it take for the object to land from the time it was thrown?


Homework Equations


I'm not sure if all of the below are relevant, or perhaps some equations are missing.

Δx = v0t + 1/2at2
(displacement = initial velocity x time + 1/2 acceleration x time squared)

vf2 = v02 + 2aΔx
(final velocity squared = initial velocity squared + 2 acceleration x displacement


The Attempt at a Solution


t1 = v/a = 1.02 s
t2 = v/a = 2.04 s
t1 + t2 = 3.1 s

Not sure how to find the displacement, but the answer key says it's -15m. How do I find it?
 
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Natko said:
Not sure how to find the displacement, but the answer key says it's -15m. How do I find it?
You can use either of your two equations to solve for the displacement. If you use the first, do not round off the time to 3.1 seconds.
 
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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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