Problem Graphic


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 m_{o}.
 The fuel has an initial mass m_{f}, and burns at a constant rate of dm_{f}/dt = c.
 The fuel is expelled from the rocket at a constant speed v_{f} relative to the rocket.
 The rocket is fired vertically from rest.
 Drag resistance of the air may be neglected.
