6. A rocket burning its onboard fuel while moving through space has velocity −→v (t) and mass m(t) at time t. If the exhaust gases escape with velocity −→v e, relative to the rocket, then md−→v /dt = dm/dt−→v e. (a) Show using this equation that −→v (t) = −→v (0) − ln(m(0)/m(t))−→v e; (b) If the rocket accelerates in a straight line from rest to twice the speed of its exhaust gases, then what fraction of its initial mass would the rocket have to burn as fuel?