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Ion-propulsion rockets have been proposed for use in space. They employ atomic ionization techniques and nuclear energy sources to produce extremely high exhaust velocities, perhaps as great as $8.00\times 10^{6}\textrm{ m/s}$ . These techniques allow a much more favorable payload-to-fuel ratio. To illustrate this fact: (a) Calculate the increase in velocity of a 20,000-kg space probe that expels only 40.0-kg of its mass at the given exhaust velocity. (b) These engines are usually designed to produce a very small thrust for a very long time—the type of engine that might be useful on a trip to the outer planets, for example. Calculate the acceleration of such an engine if it expels $4.50\times 10^{-6}\textrm{ kg/s}$ at the given velocity, assuming the acceleration due to gravity is negligible.
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Final Answer
  1. $1.60\times 10^{4}\textrm{ m/s}$
  2. $1.80\times 10^{-3}\textrm{ m/s}^2$
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OpenStax College Physics Solution, Chapter 8, Problem 56 (Problems & Exercises) (3:57)

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