Two astronauts at rest face each other in space. One, with mass m1, throws a ball of mass mb the other, whose mass is m2. She catches the ball and throws is back to the first astronaut following each throw the ball has a speed of v relative to the thrower. Let the direction that Astronaut 1 first throw the ball to the positive direction.  After each has made one throw and one catch how fast are the astronauts moving? How much has the two-astronaut system’s kinetic energy changed  Where did the energy come from?

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