Question

Consider a rocket that is in deep space and at rest relative to an inertial reference frame. the rocket's engine is to be fired for a certain interval. (a) what must be the rocket's mass ratio (ratio of initial to final mass) over that interval if the rocket's original speed relative to the inertial reference frame is to be equal to the exhaust speed

Answer 1

Solution: u = exhaust speed wrt rocket. Mt conservation: instant t: vm. Instant t+dt (v+dv)(m-dm)+(u+v)dm (dm >0,u<0) Conservation (1st order) dvm +udm =0 or dm/m = -dv/u Log(m/m0) = -1/u Vfinal Vfinal = -uLog(m/m_0) = u Log(m_0/m) so if you want v = u (in absolute value) m_0/m =e=2.718 and for v=9u, m_0/m = e^9 = 8103