Consider a rocket that is in deep space and at rest

Chapter , Problem 78

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Consider a rocket that is in deep space and at rest relative to an inertial reference frame. The rockets engine is to be fired for a certain interval. What must be the rockets mass ratio (ratio of initial to final mass) over that interval if the rockets original speed relative to the inertial frame is to be equal to (a) the exhaust speed (speed of the exhaust products relative to the rocket) and (b) 2.0 times the exhaust speed?

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