Finding jumping height on an unknown planet given Mass/Radius

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To determine how high one can jump on an unknown planet with a mass of 4.19*10^21 kg and a radius of 1*10^6 m, the gravitational acceleration was calculated to be 0.28 m/s². The discussion revolves around using gravitational potential energy equations to relate jump heights on Earth and the unknown planet. It was established that the energy source for jumping remains constant, allowing the application of conservation of energy principles. By substituting the gravitational acceleration into the jump height formula, a jump height of 35 meters was derived for the unknown planet. The conversation emphasizes the importance of understanding gravitational effects when comparing different celestial bodies.
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Homework Statement


Knowing you can jump about 1m high on Earth's surface, how high can you jump on the unknown planet.
Munknown= 4.19*10^21kg
Radius Unknown= 1*10^6m

Homework Equations


Not sure if can be used in this question
K1+U1 = K2 + U2
1/2MV2 + mgh = 1/2MV2 + mgh
U=-GM/r and U = mgh
g=GM/R2

The Attempt at a Solution


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I found the force of gravity on the unknown planet using GM/R2
Giving me 0.28m/s2
Can I just equate the two equations for Gravitional Potential energy (U) to find the new height? as in -GM/r = mgh?
 
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rkiecaboose said:
Can I just equate the two equations for Gravitional Potential energy (U) to find the new height?

If you were to do that, you are saying that the initial energy on each planet is the same.
Is it?
 
rkiecaboose said:

Homework Statement


Knowing you can jump about 1m high on Earth's surface, how high can you jump on the unknown planet.
Munknown= 4.19*10^21kg
Radius Unknown= 1*10^6m

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How do the mass & radius of Planet X compare to those of Earth?

Do you know Newton's law of universal gravitation ?

Added in Edit:

I see that you did add some information after I quoted the OP.
 
Sorry I posted the question initially while I went and grabbed my work.
Newtons universal law of gravitation...
F=GM1M2/R2
Though I don't know where I would use it.
Am I on the right track using conservation of energy but instead of using mgh use -GM/r ?
 
Villyer said:
If you were to do that, you are saying that the initial energy on each planet is the same.
Is it?

Well if we're considering the initial point to be grounded wouldn't the initial just be 0 on both planets? I'm lost as to how to relate Earth to the unknown
 
rkiecaboose said:
Well if we're considering the initial point to be grounded wouldn't the initial just be 0 on both planets? I'm lost as to how to relate Earth to the unknown

Were does the energy that makes a person jump come from?

Does this source maintain its full potential when transferred to a planet with different gravity?
 
I think the energy stored in one's muscle must be the same everywhere.
 
So...can someone tell me if this is correct?
Since I know the gravitational potential energy (U) is mgh on earth. It gives me 490J assuming a mass of 50kg. I used the same equation U=mgh, solving for h gives: U/mg=h.
Since the gravitational acceleration is GM/R2 the acceleration on the new planet is 0.28m/s2. I just plugged it into give me a jump height of 35m.
 
You can check about Apollo astronauts jumping on the surface of the moon.
Conservation of energy applies everywhere.
 
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