Is it possible to find the answer?

[phys1618]

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.

 

[Copycat91]

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.