When designing rockets to transport a given payload into space, rocket scientists must determine the optimal mass of fuel for the rocket to carry. How can they determine the maximum velocity a rocket will attain based on the amount of fuel it carries?
What is known:
- The total initial mass of a rocket and its fuel is mo.
- The fuel has an initial mass mf, and burns at a constant rate of dmf/dt = c.
- The fuel is expelled from the rocket at a constant speed vf relative to the rocket.
- The rocket is fired vertically from rest.
- Drag resistance of the air may be neglected.