Calculate height given KE and mass

[Sandman327]

Homework Statement

At sea level a nitrogen molecule in the air has an average translational KE of 6.2x10-21 J. Its mass is 4.7x10-26 kg. If the molecule could shoot straight up without striking other air molecules, how high would it rise? Thanks for any help.

Homework Equations

I think to find height I should use the equation U=mgy but I'm not 100% sure because I don't understand how KE relates to U.

The Attempt at a Solution

I set the equation up so that y=U/mg and I get the answer 13460.7m which just seems to big to be right although I could be wrong about that.

 

[RoyalCat]

Draw a diagram of the initial and final states of the nitrogen molecule.
What's the energy in the initial state, and what's the energy in the final state? How do these two relate?

Your final answer is most likely correct (Number crunching errors aside), and I'm glad you see the importance of understanding how you got to it.

 

[tiny-tim]

Welcome to PF!

Hi Sandman327! Welcome to PF!

… I don't understand how KE relates to U.

It's very simple:

always remember this formula … KE + PE = constant

 

[Amar.alchemy]

since it doesn't loose any energy by striking the other molecules, the entire KE will be converted into PE by raising to the height 13460.7m...