Question

A balloonist happens to drop his metal ballpoint pen from his balloon as he is taking notes on his flight. Because his pen has a streamlined shape, air resistance has little effect on its fall. The pen strikes the ground at 22 m/s. How high was the balloon?

Answer 1

So this is dealing with the conservation of energy. So you set kinetic energy equal to potential energy, so it looks like this:

1/2mv^2=mgh. The m's cancel out, so it is 1/2v^2=gh.

To find out what the height h is, divide g on both sides, so...

h=0.5v^2/g. v=22m/s, g=9.81m/s^2, so h=(0.5)(22^2)/(9.81)=24.67m