A bullet is fired straight up into the air with an initial speed of 450 m/s. To what maximum height will the bullet reach?

Hello!

This question is relatively simple to answer if we ignore air resistance. But actually in this case it will be a very rough estimate, because such a great initial speed means huge air resistance.

I hope this is a sample problem about a free fall and that you don't need to use the result in practice.

The simplest method to find the maximum height, denote it is to consider energy (also denote the initial speed as ). If we measure potential energy off of the ground level, then at the start a bullet has only kinetic energy   At the maximum height, when a bullet starts to fall, the speed will be zero, and a bullet has only potential energy

Because of energy conservation    so

=10125 (m). This is the formal answer. In reality it will be much less, when taking air resistance into consideration.