Is it possible to find the answer?

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AI Thread Summary
Jumping into a hole through the Earth would involve gravitational acceleration, initially pulling the jumper down at 9.8 m/s². As the jumper reaches the center of the Earth, acceleration ceases, but velocity remains. The motion can be modeled as simple harmonic oscillation, allowing for calculations of the time taken to traverse the Earth. The gravitational acceleration can be determined using the formula g' = GMr/R³, where r is the distance from the center. Ultimately, it is indeed possible to calculate the time it takes to reach the other side of the Earth.
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Homework Statement



if you dig a hole through earth, all the way through so you can see the other side is space. and you decided to jump into it. How long does it take for you to get to the other sisde of earth?

Homework Equations


the distance from top to bottom of Earth is 4000mi.


The Attempt at a Solution


I know that once you jump into the earth, gravity which is 9.8m/s will pull you down quickly. However, once you are directly in the middle of earth, you would stop accelerating. so is it possible to figure the answer? thank you for all help and inputs.
 
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Yes, it is.
In the middle of earth, no acceleration, but we still have velocity.
You can use gravitational acceleration inside of earth:
[TAB]g'=GMr/R^3
where r is distance from center of earth, R is Earth's radius, and M is Earth's mass.
It's just like a simple harmonic oscillation.
 
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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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