A rocket of initial mass mo and zero initial velocity ejects exhaust at a constant velocity vex relative to itself in outer space (no gravity).

1) Using conservation of momentum, derive the "rocket equation" for the rocket velocity v as a function of the residual mass m of the rocket. Explain why space engineers use multistage rockets.

2) 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.

3) 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.

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