Calculating acceleration of gravity on a planet

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To calculate the acceleration of gravity on a planet based on an astronaut's jump, the initial speed and maximum horizontal distance are critical. The astronaut jumps 30 meters with an initial speed of 9 m/s, leading to a calculated acceleration of -1.35 m/s². However, the discussion highlights that the kinematic equation used is only applicable for one-dimensional motion and does not account for the two-dimensional nature of projectile motion. It emphasizes the importance of considering both horizontal and vertical components and suggests reviewing the Range Equation for a more accurate analysis. Understanding the optimum launch angle is also essential for maximizing projectile range.
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Homework Statement


An astronaut on a strange planet finds that he can jump a maximum horizontal distance of 30m if his initial speed is 9m/s. What is the acceleration of gravity on the planet?

Homework Equations


Vf^2=Vi^2+2a(Xf-Xi)

The Attempt at a Solution


I used the formula mentioned above, plugged in number
Vf=0m/s
Vi=9m/s
X=Xf-Xi=30m
and get a=-1.35m/s^2

I'm not sure if it is correct, could someone double check and tell me if I did anything wrong? Thanks
 
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Consider the trajectory of the jump: It's not a one-dimensional linear motion but rather a 2D curve, one with both horizontal and vertical components. The kinematic equation that you've chosen applies to motion in one dimension and doesn't take into account splitting the given velocity into components.

What's the optimum launch angle to maximize the range of a projectile? Have you covered the Range Equation in your classes? (If not you might want to look it up and try to remember it; it can really come in handy to avoid re-deriving the range of a projectile every time).
 
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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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