A rocket of initial mass M0 and zero initial velocity ejects exhaust at a constant velocity V_ex relative to itself in outer space -- no gravity.

1) If the above rocket ejects mass at a constant rate: dm / dt = -c,

Find the rocket's distance traveled as a time function -- use integral for ln(t), and Discuss the limit when m 0.

2) A long rigid massless rod of length L connects two rockets of initial mass M0 and infinitesimal size at opposite ends. If the two rockets eject gas with constant exhaust velocity V_ex in opposite directions perpendicular to the rod, draw the figure and find the angular velocity as a function of each rocket's residual mass m.