# Hover jet

A jump jet of mass $\SI{400}{\kilogram}$ (without fuel) can hover, stationary, by burning fuel and blasting the waste products downwards at a constant velocity of $\SI[per-mode=symbol]{1000}{\meter \per \second}$ (relative to the jet). It is carrying $\SI{100}{\kilogram}$ of fuel.

How long, in seconds, can the jump jet hover like this before it runs out of the fuel?

Assume that the fuel contains all of the reactants: i.e. no air is being drawn from outside. (A real jump jet would take in air from outside, which would make up a substantial fraction of the exhaust mass.)

Take the acceleration due to gravity to be $\SI[per-mode=symbol]{10}{\meter \per \second \squared}$.