8. Suppose rockets were used to launch the satellite from the north pole to its orbit, how much work did the rockets do? (Neglect any change in mass due to fuel ejection.) 1 GmM 1 GmM 3 GMM GmM A) B) C). D) 4 R 2 R 4 R R

Professional Application 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 8.00106 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 4.50106 kg/s at the given velocity, assuming the acceleration due to gravity is negligible.

Professional Application Calculate the increase in velocity of a 4000-kg space probe that expels 3500 kg of its mass at an exhaust velocity of 2.00103 m/s. You may assume the gravitational force is negligible at the probe's location.

An average-sized asteroid located 5.0107km from Earth with mass 2.01013kg is detected headed directly toward Earth with speed of 2.0km/s . What will its speed be just before it hits our atmosphere? (You may ignore the size of the asteroid.)