How High Could a Person Jump on Pluto Compared to Earth?

AI Thread Summary
The discussion centers on calculating how high a person could jump on Pluto compared to Earth, given that the initial jump velocity remains constant. Key information includes Pluto's mass and radius, which are necessary to determine its gravitational acceleration. Participants note that much of the provided data is extraneous for the specific question of jump height. The focus is on deriving the gravitational force on Pluto to compare it with Earth's gravity. Ultimately, understanding Pluto's gravity is essential to solving the problem of jump height.
lawfulgm
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Homework Statement


Pluto is only planet that has not yet been visited by a spacecraft . Pluto has a mass of 1.27*10^22 kg and a radius of 1.14*10^6m. although Pluto is in an elliptical orbit about the sun, for simpicity we'll assume Pluto orbits the sun in a circular orbit of radius 5.91*10^12 m. the mass of the sun is 1.99 * 10^30


Homework Equations


The question is...
If generic man can jump to height h on Earth, how high chould generic man jump on Pluto, assuming his initial veocity is the same on both planets?


The Attempt at a Solution

 
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How many of those things you are given are relevant to "how high" the man can jump?
 
HallsofIvy said:
How many of those things you are given are relevant to "how high" the man can jump?

The question did not mention about that. It just said the man can jump "h" meter.
 
You're given a hell of a lot more information than needed in here. How can you figure out the acceleration of gravity on Pluto using the information provided?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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