Is it more energy efficient to throw a large object slower than a slower object faster? For example, suppose a 100kg person out in space threw a 10 kg object away from themselves at 1 m/s. that means that the 100 kg person would move in the opposite direction at .1 m/s. And this should take (.5*10kg*1^2) equals 5 Joules to throw the 10 kg object and send the astronaut traveling at .1m/s. Now if that astronaut threw a 1kg object away from themselves at 10m/s then this would also send the astronaut traveling away at .1m/s but... the energy to throw this smaller object faster would be (.5*1kg*10^2) equal to 50 Joules. So it would seem that it would take 10 times the energy for the astronaut to travel at the same speed? Is this correct? I understand that kinetic energy isn't conserved but momentum is conserved. I am just interested in terms of e.g. fuel efficiency.